Mastering Physics Solutions Chapter 22 Magnetism
Chapter 22 Magnetism Q.1CQ
Two charged particles move at light angles to a magnetic field and deflect in opposite directions Can one conclude that the particles have opposite charges?
Solution:
No
The particles may have charge of the same sign but move in opposite directions along the same lina In this way, they would both move perpendicular to the field, but would deflect in opposite direction.
Chapter 22 Magnetism Q.1P
CE Predict/Explain Proton 1 moves with a speed v from the east coast to the west coast in the continental United States; proton 2 moves with the same speed from the southern United States toward Canada. (a) Is the magnitude of the magnetic force experienced by proton 2 greater than, less than, or equal to the force experienced by proton 1? (b) Choose the best explanation from among the following:
I. The protons experience the same force because the magnetic field is the same and their speeds are the same.
II. Proton 1 experiences the greater force because it moves at right angles to the magnetic field.
III. Proton 2 experiences the greater force because it moves in the same direction as the magnetic field.
Solution:
Chapter 22 Magnetism Q.2CQ
An electron moves with constant velocity through a region of space that is free of magnetic fields. Can one conclude that the electric field is zero in this region? Explain.
Solution:
Ans:
Yes,
If an electric field exist in this region of space, and no magnetic field is present, the electric field will exert a force on the electron and causes it to accelerate.
Chapter 22 Magnetism Q.2P
CE An electron moves west to east in the continental United States Does the magnetic force experienced by the electron point ma direction that is generally north. south, east, west. upward. or downward? Explain
Solution:
Recall the Earth has its own magnetic fiela The field generated is similar to the one generated by a bar magnet with its pole near to the geographical pole of the EarthS Currently. the magnetic
north is located in northern Canada So. the magnetic field in the continental United States points primarily towards the north Consider an electron moving from west to east in the continental United States The velocity vector will point towards east and magnetic field point towards north
Use the right hand rule to find the direction of magnetic force. According to right hand rule, the direction of magnetic force will be the direction of your thumb when you curl your right hand
fingers from velocity vector to magnetic field vector So. here by right hand rule, the magnetic force will be towards upwards. However here the particle is an electron which is a negatively
charged particle. So. reverse the direction found by right hand rule to get the true direction of magnetic force. Therefore, here the magnetic force is on the electron is downwards
Chapter 22 Magnetism Q.3CQ
An electron moves with constant velocity through a region of space that is Free of electric fields. Can one conclude that the magnetic field is zero in this region? Explain.
Solution:
Chapter 22 Magnetism Q.3P
CE An electron moving in the positive x direction, at right angles to a magnetic field. experiences a magnetic force in the positive y direction What is the direction of the magnetic field?
Solution:
An electron moving in the positive x-direction at right angles to a magnetic field, experiences a magnetic force in the positive y-direction The magnetic field is in the positive z-direction
Chapter 22 Magnetism Q.4CQ
Describe how the motion of a charged particle can be used to distinguish between an electric and a magnetic field
Solution:
In a uniform electric field, the force on a charged particle is always in the same direction, leading to parabolic trajectories In a uniform magnetic field, the force of charged particles is always right angles to the motion, resulting the circular paths (or) helical trajectories
Perhaps even more important. a charged particle experiences a force due to an electric field whether it is moving (or) at rest in the magnetic field, the particle must be moving to experience a force.
Chapter 22 Magnetism Q.4P
Solution:
Chapter 22 Magnetism Q.5CQ
Explain how a charged particle moving in a circle of small radius can take the same amount of time to complete an orbit as an identical particle orbiting in a circle of large radius.
Solution:
The radius of curvature is proportional to the speed of the par1icle It follows that the particle moving in a circle of large radius has a proportionally larger speed than the particle moving in a
circle of small radius. Therefore, the time required for an orbit (t=d/v) is the same for both particles
Chapter 22 Magnetism Q.5P
Solution:
Apply the concept of force on a moving charged particle in uniform magnetic field. Apply the right hand rule to find the charge of the deflecting particle in the uniform magnetic field.
From right hand rule, the direction of the particle in the uniform magnetic field depends on its sign. The force exerted on a negatively charged particle is opposite in direction to the force exerted on a positively charged particle.
For particle A: Initially place the fingers of right hand in the direction of motion of the particle. As the fingers of right hand curls in the direction of the magnetic field that is outward, the thumb points downward. The downward deflection force is for a positively charged particle. Since the deflecting force on the particle is directed up, the charged particle A must be negative.
For particle B: Initially place the fingers of right hand in the direction of motion of the particle. As the fingers of right hand curls in the direction of the magnetic field that is outward, the thumb points downward. The downward deflection force is for a positively charged particle. Since the deflecting force on the particle is directed up, the charged particle B must be negative.
For particle C: Initially place the fingers of right hand in the direction of motion of the particle. As the fingers of right hand curls in the direction of the magnetic field that is outward, the thumb points downward. The downward deflection force is for a positively charged particle. Since the deflecting force on the particle is directed down, the charged particle C must be positive.
Chapter 22 Magnetism Q.6CQ
A current-carrying wire is placed in a region with a uniform magnetic field. The wire experiences zero magnetic force. Explain.
Solution:
Chapter 22 Magnetism Q.6P
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Chapter 22 Magnetism Q.7P
What is the acceleration of a proton moving with a speed of 6.5 m/s at right angles to a magnetic field of 1.6 T?
Solution:
Chapter 22 Magnetism Q.8P
An electron moves at right angles to a magnetic field of 0.18 T. What is its speed if the force exerted on it is 8.9 × 1015 N?
Solution:
Chapter 22 Magnetism Q.9P
A negatively charged ion moves due north with a speed of 1.5 × 106 m/s at the Earth’s equator. What is the magnetic force exerted on this ion?
Solution:
Chapter 22 Magnetism Q.10P
A proton high above the equator approaches the Earth moving straight downward with a speed of 355 m/s. Find the acceleration of the proton, given that the magnetic field at its altitude is 4.05 × 10−5 T.
Solution:
Chapter 22 Magnetism Q.11P
A 0.32-μ C particle moves with a speed of 16 m/s through a region where the magnetic field has a strength of 0.95 T. At what angle to the field is the particle moving if the force exerted on it is (a) 4.8 × 10−6 N, (b) 3.0 × 10−6, or (c) 1.0 × 10−7 N?
Solution:
Chapter 22 Magnetism Q.12P
A particle with a charge of 14 μ C experiences a force of 2.2 × 10−4 N when it moves at right angles to a magnetic field with a speed of 27 m/s. What force does this particle experience when it moves with a speed of 6.3 m/s at an angle of 25° relative to the magnetic field?
Solution:
Chapter 22 Magnetism Q.13P
An ion experiences a magnetic force of 6.2 × 10−16 N when moving in the positive × direction but no magnetic force when moving in the positive y direction. What is the magnitude of the magnetic force exerted on the ion when it moves in the x−y plane along the line × = y? Assume that the ion’s speed is the same in all cases.
Solution:
Chapter 22 Magnetism Q.14P
An electron moving with a speed of 4.2 × 105 m/s in the positive × direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.0 × 10−13 N that points in the negative z direction. What are the direction and magnitude of the magnetic field?
Solution:
Chapter 22 Magnetism Q.15P
IP Two charged particles with different speeds move one at a time thro ugh a region of uni form magnetic field. The particles move in the same direction and experience equal magnetic forces, (a) If particle 1 has four tunes the charge of particle 2 which particle has the greater speed? Explain, (b) Find the ratio of the speeds, v1/v2.
Solution:
Chapter 22 Magnetism Q.16P
A 6.60-μ C particle moves through a region of space where an electric field of magnitude 1250 N/C points in the positive x direction, and a magnetic field of magnitude 1.02 T points in the positive z direction. If the net force acting on the particle is 6.23 × 10−3 N in the positive x direction, find the magnitude and direction of the particle’s velocity. Assume the particle’s velocity is in the x-y plane.
Solution:
Chapter 22 Magnetism Q.17P
When at rest, a proton experiences a net electromagnetic force of magnitude 8.0 × 10−13 N pointing in the positive x direction. When the proton moves with a speed of 1.5 × 106 m/s in the positive y direction, the net electromagnetic force on it decreases in magnitude to 7.5 × 10−13 N, still pointing in the positive x direction. Find the magnitude and direction of (a) the electric field and (b) the magnetic field.
Solution:
Chapter 22 Magnetism Q.18P
CE A velocity selector is to be constructed using a magnetic field in the positive y direction. If positively charged particles move through the selector in the positive z direction, (a) what must be the direction of the electric field? (b) Repeat part (a) for the case of negatively charged particles.
Solution:
A positive charge always moves along the direction of electric field, but a negative charge moves opposite to the direction of electric field. Hence, from this we can say that the direction of electric field is opposite to the direction of motion of negative charge.
(a)
According to Right Hand Rule, if the direction of velocity of the positive charged particles is in positive z-direction and the direction of magnetic field is in positive y- direction then the direction of electric field is in positive x-direction.
(b)
According to Right Hand Rule, if the direction of velocity of the negative charged particles is in positive z-direction and the direction of magnetic field is in positive y- direction then the direction of electric field is in positive x-direction.
Chapter 22 Magnetism Q.19P
Find the radius of an electron’s orbit when it moves perpendicular to a magnetic field of 0.66 T with a speed of 6.27 × 105 m/s.
Solution:
Chapter 22 Magnetism Q.20P
Find the radius of a proton’s orbit when it moves perpendicular to a magnetic field of 0.66 T with a speed of 6.27 × 105 m/s.
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Chapter 22 Magnetism Q.21P
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Chapter 22 Magnetism Q.22P
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Chapter 22 Magnetism Q.23P
IP BIO The artery in Figure 22–11 has an inside diameter of 2,75 mm and passes through a region where the magnetic field is 0.065 T. (a) If the voltage difference between the electrodes is 195 μ V, what is the speed of the blood? (b) Which electrode is at the higher potential? Does your answer depend on the sign of the ions in the blood? Explain.
Solution:
Chapter 22 Magnetism Q.24P
An electron accelerated from rest through a voltage of 550 V enters a region of constant magnetic field, ff the electron follows a circularpath with a radius of 17 cm, what is the magnitude of the magnetic field?
Solution:
Chapter 22 Magnetism Q.25P
A 12.5-μC particle with a mass of 2.80 × 10−5 kg moves perpendicular to a 1.01-T magnetic field in a circular path of radius 21.8 m. (a) How fast is the particle moving? (b) How long will it take the particle to complete one orbit?
Solution:
Chapter 22 Magnetism Q.26P
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Chapter 22 Magnetism Q.27P
A proton with a kinetic energy of 4.9 × 10 –16 J moves perpendicular to a magnetic field of 0.26 T. What is the radius of its circular path?
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Chapter 22 Magnetism Q.28P
IP An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of 6.64 × 10−27 kg. A horizontal beam of alpha particles is injected with a speed of 1.3 × 105 m/s into a region with a vertical magnetic field of magnitude 0.155 T. (a) How long does it take for an alpha particle to move halfway through a complete circle? (b) if the speed of the alpha particle is doubled, does the time found in part (a) increase, decrease, or stay the same? Explain, (c) Re-peat part (a) for alpha particles with a speed of 2.6 × 105 m/s.
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Chapter 22 Magnetism Q.29P
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Chapter 22 Magnetism Q.30P
What is the magnetic force exerted on a 2.15-m length of wire carrying a current of 0.899 A perpendicular to a magnetic field of 0.720 T?
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Chapter 22 Magnetism Q.31P
A wire with a current of 2.8 Ais at an angle of 36.0° relative to a magnetic field of 0.88 T. Find the force exerted on a 2.25-m length of the wire.
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Chapter 22 Magnetism Q.32P
The magnetic force exerted on a 1.2-m segment of straight wire is 1.6 N. The wire carries a current of 3.0 A in a region with a constant magnetic field of 0.50 T. What is the angle between the wire and the magnetic field?
Solution:
Chapter 22 Magnetism Q.33P
A 0.45-m copper rod with a mass of 0.17 kg carries a current of 11 A in the positive × direction. What are the magnitude and direction of the minimum magnetic field needed to levitate the rod?
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Chapter 22 Magnetism Q.34P
A wire with a length of 3.6 m and a mass of 0.75 kg is in a region of space with a magnetic field of 0.84 T. What is the minimum current needed to levitate the wire?
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Chapter 22 Magnetism Q.35P
A wire with a length of 3.6 m and a mass of 0.75 kg is in a region of space with a magnetic field of 0.84 T. What is the minimum current needed to levitate the wire?
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Chapter 22 Magnetism Q.36P
A high-voltage power Une carries a current of 110 A at a location where the Earth’s magnetic field has a magnitude of 0.59 G and points to the north, 72° below the horizontal. Find the direction and magnitudeof the magnetic force exerted on a 250-m length of wire if the current in the wire flows (a) horizontally toward the east or (b) horizontally toward the south.
Solution:
Chapter 22 Magnetism Q.37P
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Chapter 22 Magnetism Q.38P
Solution:
a) The force on the left vertical wire is out of the page, the force on the right vertical wire is into the page; the horizontal wire experiences zero force. As a result, the loop tends to rotate counter clockwise, as viewed from above.
b) This loop tends to rotate clockwise
c) This loop will not tend to rotate at all
Chapter 22 Magnetism Q.39P
A rectangular loop of 260 turns is 33 cm wide and 16 cm high. What is the · tuent in this loop if the maximum torque in a field of 0.48 T is 23 N · m?
Solution:
Chapter 22 Magnetism Q.40P
A single circular loop of radius 0.23 m carries a current of 2.6 Ain a magnetic field of 0.95 T. What is the maximum torque exerted on this loop?
Solution:
Chapter 22 Magnetism Q.41P
In the previous problem, find the angle the plane of the loop must make with the field if the torque is to be half its maximum value.
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Chapter 22 Magnetism Q.42P
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Chapter 22 Magnetism Q.43P
IP Two current loops, one square the other circular, have one turn made from wires of the same length. (a) If these loops carry the same current and are placed in magnetic fields of equal magnitude, is the maximum torque of the square loop greater than, less than, or the same as the maximum torque of the circular loop? Explain. (b) Calculate the ratio of the maximum torques, τsquare/τcirclc.
Solution:
Chapter 22 Magnetism Q.44P
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Chapter 22 Magnetism Q.45P
· Find the magnetic field 6.25 cm from a long, straight wire that carries a current of 7.81 A.
Solution:
Chapter 22 Magnetism Q.46P
A long, straight wire carries a current of 7.2 A. How far from this wire is the magnetic field it produces equal to the Earth’s magnetic field, which is approximately 5.0 × 10−5 T?
Solution:
Chapter 22 Magnetism Q.47P
You travel to the north magnetic pole of the Earth, where the magnetic field points vertically downward. There, you draw a circle on the ground. Applying Ampere’s law to this circle show that zero current passes through its area.
Solution:
Chapter 22 Magnetism Q.48P
Two power lines, each 270 m in length, runparallel to each other with a separation of 25 cm. If the lines carry parallel currents of 110 A, what are the magnitude and direction of the magnetic force each exerts on the other?
Solution:
Chapter 22 Magnetism Q.49P
· BIO Pacemaker Switches Some pacemakers employ magnetic reed switches to enable doctors to change their mode of operation without surgery. A typical reed switch can be switched from one position to another with a magnetic field of 5.0 × 10−4 T. What current must a wire carry if it is to produce a 5.0 × 10−4 T field at a distance of 0.50 m?
Solution:
Chapter 22 Magnetism Q.50P
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Chapter 22 Magnetism Q.51P
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Chapter 22 Magnetism Q.52P
In Oersted’s experimen t, suppose that the compass was 0.25 m from the current-carrying wire. If a magnetic field of half the Earth’s magnetic field of 5.0 × 10−5 T was required to give a noticeable deflection of the compass needle, what current must the wire have carried?
Solution:
Chapter 22 Magnetism Q.53P
IP Two long, straight wires are separated by a distance of 9.25 cm. One wire carries a current of 2.75 A, the other carries a current of 4.33 A. (a) Find the force per meter exerted on the 2.75-A wire, (b) Is the force per meter exerted on the 4.33-A wire greater than, less than, or the same as the force per meter exerted on the 2.75-A wire? Explain.
Solution:
Chapter 22 Magnetism Q.54P
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Chapter 22 Magnetism Q.55P
Solution:
Use the concept of the right hand rule to find the direction of the electric current passing through the loop. The conventional current direction is always from the positive terminal to the negative terminal.
The loop creates the North Pole towards the south pole of the bar magnet as the loop attracts the bar magnet. From the right hand rule, the current in the loop is in a counter clockwise direction. Since the conventional current is always directed from the positive terminal, the terminal A must be positive of the battery.
Chapter 22 Magnetism Q.56P
· CE Predict/Explain The number of turns in a solenoid is doubled, and at the same time its length is doubled. Does the magnetic field within the solenoid increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Doubling the number of turns in a solenoid doubles its magnetic field, and hence the field increases.
II. Making a solenoid longer decreases its magnetic field, and therefore the field decreases.
III. The magnetic field remains the same because the number of turns per length is unchanged.
Solution:
Chapter 22 Magnetism Q.57P
It is desired that a solenoid 38 cm long and with 430 turns produce a magnetic field within it equal to the Earth’s magnetic field (5.0 × 10−5 T). What current is required?
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Chapter 22 Magnetism Q.58P
A solenoid that is 62 cm long produces a magnetic field of 1.3 T within its core when it carries a current of 8.4 A. How many turns of wire are contained in this solenoid?
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Chapter 22 Magnetism Q.59P
The maximum current in a superconducting solenoid can be as large as 3.75 kA. If the number of turns per meter in such a solenoid is 3650, what is the magnitude of the magnetic field it produces?
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Chapter 22 Magnetism Q.60P
To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12 cm in diameter and 55 cm in length. You would like a 2.0-A current to produce a 2.5-kG magnetic field inside your solenoid. What is the total length of wire you will need to meet these specifications?
Solution:
Chapter 22 Magnetism Q.61GP
CE At a point near the equator, the Earth’s magnetic field is horizontal and points to the north. If an electron is moving vertically upward at this point, does the magnetic force acting on it point north, south, east, west, upward, or downward? Explain.
Solution:
At a point near the equator, the Earth’s magnetic field is horizontal and points to the north. If the electron is moving vertically upward at this point, the magnetic force acting on the electron points to the east.
Chapter 22 Magnetism Q.62GP
CE A proton is to orbit the Earth at the equator using the Earth’s magnetic field to supply part of the necessary centripetal force. Should the proton move eastward or westward? Explain.
Solution:
The Earth’s magnetic field will be directed towards north at the equator. The necessary centripetal force to the proton has to be provided by the magnetic field of the earth. As the centripetal force is to be in the outward direction, the direction of the magnetic force will be in the inward direction. Therefore, from Fleming’s left hand rule, the proton has to move in the westward direction in order to orbit the earth at the equator.
Chapter 22 Magnetism Q.63GP
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Chapter 22 Magnetism Q.64GP
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Chapter 22 Magnetism Q.65GP
CE Each of the current-carrying wires in Figure 22–42 is long and straight, and carries the current I either into or out of the page, as shown. What is the direction of the net magnetic field produced by these three wires at the center of the triangle?
Solution:
Chapter 22 Magnetism Q.66GP
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Chapter 22 Magnetism Q.67GP
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Chapter 22 Magnetism Q.68GP
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Chapter 22 Magnetism Q.69GP
A stationary proton (q = 1.60 × 10−19 C) is Located between the poles of a horseshoe magnet, where the magnetic field is 0.35 T. What is the magnitude of the magnetic force acting on the proton?
Solution:
Chapter 22 Magnetism Q.70GP
BIO Brain Function and Magnetic Fields Experiments have shown that thought processes in the brain can be affected if the parietal lobe is exposed to a magnetic field with a strength of 1.0 T. How much current must a long, straight wire carry if it is to produce a 1.0-T magnetic field at a distance of 0.50 m? (For comparison, a typical lightning bolt carries a current of about 20,000 A, which would melt most wires.)
Solution:
Chapter 22 Magnetism Q.71GP
A mixture of two isotopes is injected into a mass spectrometer. One isotope follows a curved path of radius R1 = 48.9 cm; the other follows a curved path of radius R2 = 51.7 cm. Find the mass ratio, m1/m2, assuming that the two isotopes have the same charge and speed.
Solution:
Chapter 22 Magnetism Q.72GP
High above the surface of the Earth, charged particles (such as electrons and protons) can become trapped in the Earth’s magnetic field in regions known as Van Alien belts. A typical electron in a Van Allen belt has an energy of 45 keV and travels in a roughly circular orbit with an average radius of 220 m. What is the magnitude of the Earth’s magnetic field where such an electron orbits?
Solution:
Chapter 22 Magnetism Q.73GP
Credit-Card Magnetic Strips Experiments carried out on the television show Mythbusters determined that a magnetic field of 1000 gauss is needed to corrupt the information on a credit card’s magnetic strip. (They also busted the myth that a credit card can be demagnetized by an electric eel or an eelskin wallet.) Suppose a long, straight wire carries a current of 3.5 A. How close can a credit card be held to this wire without damaging its magnetic strip?
Solution:
Chapter 22 Magnetism Q.74GP
Superconducting Solenoid Cryomagnetics, Inc., advertises a high-field, superconducting solenoid that produces a magnetic field of 17 T with a current of 105 A. What is the number of turns per meter in this solenoid?
Solution:
Chapter 22 Magnetism Q.75GP
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Chapter 22 Magnetism Q.76GP
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Chapter 22 Magnetism Q.77GP
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Chapter 22 Magnetism Q.78GP
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Chapter 22 Magnetism Q.79GP
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Chapter 22 Magnetism Q.80GP
BIO Magnetic Resonance Imaging An MR1 (magnetic resonance imaging) solenoid produces a magnetic field of 1.5 T. The solenoid is 2.5 m long, 1.0 m in diameter, and wound with insulated wires 2.2 mm in diameter. Find the current that flows in the solenoid. (Your answer should be rather large. A typical MR1 solenoid uses niobium-titanium wire kept at liquid helium temperatures, where it is superconducting.)
Solution:
Chapter 22 Magnetism Q.81GP
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Chapter 22 Magnetism Q.82GP
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Chapter 22 Magnetism Q.83GP
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Chapter 22 Magnetism Q.84GP
IP Medical X-rays An electron hi a medical X-ray machine is accelerated from rest through a vol tage of 10.0 kV. (a) Find the maximum force a magnetic field of 0.957 T can exert on this electron. (b) If the voltage of the X-ray machine is increased, does the maximumforce found in part (a) increase, decrease, or stay the same? Explain. (c) Repeat part (a) for an electron accelerated through a potential of 25.0 kV.
Solution:
Chapter 22 Magnetism Q.85GP
A particle with a charge of 34 μC moves with a speed of 73 m/s in the positive x direction. The magnetic field in this region of space has a component of 0.40 T inthe positive y direction, and a component of 0.85 T in the positive z direction. What are the magnitude and direction of the magnetic force on the particle?
Solution:
Chapter 22 Magnetism Q.86GP
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Chapter 22 Magnetism Q.87GP
IP A charged particle moves in a horizontal plane with a speed of 8.70 × 106 m/s. When this particle encounters a uniform magnetic field in the vertical direction it begins to move on a circular path of radius 15.9 cm. (a) If the magnitude of the magnetic field is 1.21 T, what is the charge-to-mass ratio (q/m)of this particle? (b) If the radius of the circular path were greater than 15.9 cm, would the corresponding charge-to-mass ratio be greater than, less than, or the same as that found in part (a)? Explain. (Assume that the magnetic field remains the same.)
Solution:
Chapter 22 Magnetism Q.88GP
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Chapter 22 Magnetism Q.89GP
Repeat Problem 88 for the case where the current in wire 1 is reversed in direction.
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Chapter 22 Magnetism Q.90GP
Lightning Bolts A powerful bolt of lightningcan carry a current of 225 kA. (a) Treating a lightning bolt as along, thin wire, calculate the magnitude of the magnetic field produced by such a bolt of lightning at a distance of 35 m. (b) ff two such bolts strike simultaneously at a distance of 35 m from each other, what is the magnetic force per meter exerted by one bolt on the other?
Solution:
Chapter 22 Magnetism Q.91GP
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Chapter 22 Magnetism Q.92GP
IP Consider the physical system shown in Figure 22—49. which consists of two current-carrying wires each with a length of 71 cm. (a) If the net magnetic field at the point A is out of the page. is the force between the wires attractive or repulsive? ExpIain (b) Calculate the magnitude of the force exerted by each wire on the other wire, given that the magnetic field at point A is out of the page with a magnitude of 2.1 x 1.0—6 T
Solution:
Chapter 22 Magnetism Q.93GP
Magnetars The astronomical object 4U014+61 has the distinction of creating the most powerful magnetic field ever observed. This object is referred to as a “magnetar” (a subclass of puisars), and its magnetic field is 1.3 × 1015 times greater than the Earth’s magnetic field. (a) Suppose a 2.5-m straight wire carrying a current of 1.1 A is placed in this magnetic field at an angle of 65° to the field lines. What force does this wire experience? (b) A field this strong can significantly change the behavior of an atom. To see this, consider an electron moving with a speed of 2.2 × 106 m/s. Compare the maximum magnetic force exerted on the electron to the electric force a proton exerts on an electron in a hydrogen atom. The radius of the hydrogen atom is 5.29 × 10−11 m.
Solution:
Chapter 22 Magnetism Q.94GP
Solution:
Chapter 22 Magnetism Q.95GP
IP A long, straight wire on the x axis carries a current of 3.12 A in the positive x direction. The magnetic field produced by the wive combines with a uniform magnetic field of 1.45 × 10−6 T that points in the positive z direction. (a) Is the net magnetic field of this system equal to zero at a point on the positive y axis or at a point on the negative y axis? Explain. (b) Find the distance from the wire to the point where the field vanishes.
Solution:
Chapter 22 Magnetism Q.96GP
Find the angle between the plane of a loop and the magnetic field for which the magnetic torque acting on the loop is equal to × times its maximum value, where 0 ≤ x ≤ 1.
Solution:
Chapter 22 Magnetism Q.97GP
Solenoids produce magnetic fields that arc relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 55 turns per centimeter, a radius of 1.0S cm, and a current of 0.622 A. (a) Find the magnetic field at the center of the solenoid. (b) What current must a long, straight wire carry to have the same magnetic field as that found in part (a)? Let the distance from the wire be the same as the radius of the solenoid, 1.05 cm.
Solution:
Chapter 22 Magnetism Q.98GP
The current in a solenoid with 22 turns per centimeter is 0.50 A. The solenoid has a radius of 1.5 cm. A long, straight wire runs along the axis of the solenoid, carrying a current of 13 A. Find the magnitude of the net magnetic field a radial distance of 0.75 cm from the straight wire.
Solution:
Chapter 22 Magnetism Q.99GP
IP BIO Transcranial Magnetic Stimulation A recently developed method to study brain function is to produce a rapidly changing magnetic field within the brain. When this technique, known as transcranial magnetic stimulation. (TMS), is applied to the prefrontal cortex, for example, it can reduce a person’s ability to conjugate verbs, though other thought processes are unaffected. The rapidly varying magnetic field is produced with a circular coil of 21 turns and a radius of 6.0 cm placed directly on the head. The current in this loop increases at the rate of 1.2 × 107 A/s (by discharging a capacitor). (a) At what rate does the magnetic field at the center of the coil increase? (b) Suppose a second coil with half the area of the first coil is used instead. Would your answer to part (a) increase, decrease, or stay the same? By what factor?
Solution:
Chapter 22 Magnetism Q.100GP
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Chapter 22 Magnetism Q.101GP
A thin ring of radius R and charge per length A rotates with an angular speed ω about an axis perpendicular to its plane and passing through its center. Find the magnitude of the magnetic field at the center of the ring.
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Chapter 22 Magnetism Q.102GP
A solenoid is made from a 25-m length of wire of resistivity 2.3 × 10−8 Ω · m. The wire, whose radius is 2.1 mm, is wrapped uniformly onto a plastic tube 4.5 cm in diameter and 1.65 m iong. Find the emf to which the ends of the wire must be connected to produce a magnetic field of 0.015 T within the solenoid.
Solution:
Chapter 22 Magnetism Q.103GP
Solution:
Chapter 22 Magnetism Q.104GP
Magnetic Fields in the Bohr Model hi the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius 5.29 × 10−11 m about the nucleus. Given that the charge on the electron is −1.60 × 10−19 C, and that its speed is 2.2 × 106 m/s, find the magnitude of the magnetic field the electron produces at the nucleus of the atom.
Solution:
Chapter 22 Magnetism Q.105GP
A single-turn square loop carries a current of 18 A. The loop is 15 cm on a side and has a mass of 0.035 kg. Initially the loop lies flat on a horizontal tabletop. When a horizontal magnetic field is turned on, it is found that only one side of the loop experiences an upward force. Find the minimum magnetic field, Bmin, necessary to start tipping the loop up from the table.
Solution:
Chapter 22 Magnetism Q.106GP
Solution:
Chapter 22 Magnetism Q.107PP
To read and understand this sentence your brain must process visual input from your eyes and translate it into words and thoughts. As you do so, minute electric currents flow through the neurons in your visual cortex. These currents, like any electric current, produce magnetic fields. In fact, even your innermost thoughts and dreams produce magnetic fields that can be detected outside your head.
Magnetoencephalography (MEG) is the study of magnetic fields produced by electrical activity in the brain. Though completely noninvasive, MEG can provide detailed information on spontaneous brain function—like alpha waves and pathological epileptic spikes—as well as brain activity that is evoked by visual, auditory, and tactile stimuli.
The magnetic fields produced by brain activity are incredibly weak—roughly 100 million times smaller than the Earth’s magnetic field. Even so, sensitive detectors called SQUIDS (superconducting quantum interference devices), which were invented by physicists as a research tool, can detect fields as small as 1.0 × 10″15 T. Coupled with sophisticated electronics and software, and operating at liquid helium temperatures (−269 °C), SQUIDS can localize the source of brain activity to within millimeters. When the information from MEG is overlaid with the anatomical data from an MRI scan, the result is a richly detailed “map” of the electrical activity within the brain.
Solution:
Chapter 22 Magnetism Q.108PP
To read and understand this sentence your brain must process visual input from your eyes and translate it into words and thoughts. As you do so, minute electric currents flow through the neurons in your visual cortex. These currents, like any electric current, produce magnetic fields. In fact, even your innermost thoughts and dreams produce magnetic fields that can be detected outside your head.
Magnetoencephalography (MEG) is the study of magnetic fields produced by electrical activity in the brain. Though completely noninvasive, MEG can provide detailed information on spontaneous brain function—like alpha waves and pathological epileptic spikes—as well as brain activity that is evoked by visual, auditory, and tactile stimuli.
The magnetic fields produced by brain activity are incredibly weak—roughly 100 million times smaller than the Earth’s magnetic field. Even so, sensitive detectors called SQUIDS (superconducting quantum interference devices), which were invented by physicists as a research tool, can detect fields as small as 1.0 × 10″15 T. Coupled with sophisticated electronics and software, and operating at liquid helium temperatures (−269 °C), SQUIDS can localize the source of brain activity to within millimeters. When the information from MEG is overlaid with the anatomical data from an MRI scan, the result is a richly detailed “map” of the electrical activity within the brain.
Solution:
Chapter 22 Magnetism Q.109PP
To read and understand this sentence your brain must process visual input from your eyes and translate it into words and thoughts. As you do so, minute electric currents flow through the neurons in your visual cortex. These currents, like any electric current, produce magnetic fields. In fact, even your innermost thoughts and dreams produce magnetic fields that can be detected outside your head.
Magnetoencephalography (MEG) is the study of magnetic fields produced by electrical activity in the brain. Though completely noninvasive, MEG can provide detailed information on spontaneous brain function—like alpha waves and pathological epileptic spikes—as well as brain activity that is evoked by visual, auditory, and tactile stimuli.
The magnetic fields produced by brain activity are incredibly weak—roughly 100 million times smaller than the Earth’s magnetic field. Even so, sensitive detectors called SQUIDS (superconducting quantum interference devices), which were invented by physicists as a research tool, can detect fields as small as 1.0 × 10″15 T. Coupled with sophisticated electronics and software, and operating at liquid helium temperatures (−269 °C), SQUIDS can localize the source of brain activity to within millimeters. When the information from MEG is overlaid with the anatomical data from an MRI scan, the result is a richly detailed “map” of the electrical activity within the brain.
Solution:
Chapter 22 Magnetism Q.110PP
To read and understand this sentence your brain must process visual input from your eyes and translate it into words and thoughts. As you do so, minute electric currents flow through the neurons in your visual cortex. These currents, like any electric current, produce magnetic fields. In fact, even your innermost thoughts and dreams produce magnetic fields that can be detected outside your head.
Magnetoencephalography (MEG) is the study of magnetic fields produced by electrical activity in the brain. Though completely noninvasive, MEG can provide detailed information on spontaneous brain function—like alpha waves and pathological epileptic spikes—as well as brain activity that is evoked by visual, auditory, and tactile stimuli.
The magnetic fields produced by brain activity are incredibly weak—roughly 100 million times smaller than the Earth’s magnetic field. Even so, sensitive detectors called SQUIDS (superconducting quantum interference devices), which were invented by physicists as a research tool, can detect fields as small as 1.0 × 10″15 T. Coupled with sophisticated electronics and software, and operating at liquid helium temperatures (−269 °C), SQUIDS can localize the source of brain activity to within millimeters. When the information from MEG is overlaid with the anatomical data from an MRI scan, the result is a richly detailed “map” of the electrical activity within the brain.
Solution:
Chapter 22 Magnetism Q.111IP
IP Referring to Example 22–3 Suppose the speed of the isotopes is doubled. (a) Does the separation distance, d, increase, decrease, or stay the same? Explain. (b) Find the separation distance for this case.
Solution:
Chapter 22 Magnetism Q.112IP
· · IP Referring to Example 22–3 Suppose we change the initial speed of 238 U, leaving everything else the same. (a) If we want the separation distance to be zero, should the initial speed of U be increased or decreased? Explain. (b) Find the required A initial speed.
Solution:
Chapter 22 Magnetism Q.113IP
Referring to Active Example 22-2 The current lx is adjusted until the magnetic field halfway between the wires has a magnitude of 2.5 × 10−6 T and points into the page. Everything else in the system remains the same as in Active Example 22–2. Find the magnitude and direction of I1.
Solution:
Chapter 22 Magnetism Q.114IP
Referring to Active Example 22-2 The current I2 is adjusted until the magnetic field 5,5 cm below wire 2 has a magnitude of 2.5 × 10−6 T and points out of page. Everything else in the system remains the same as in Active Example 22–2. Find the magnitude and direction of I2
Solution:
