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{{Chapter 27Chapter 27

Magnetic Fields and Forces (cont.)Magnetic Fields and Forces (cont.)

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Force and torque on a current loopForce and torque on a current loop• The net force on a current loop in a uniform magnetic field is The net force on a current loop in a uniform magnetic field is

zero. But the net torque is not, in general, equal to zero.zero. But the net torque is not, in general, equal to zero.• Figure 27.31 below shows the forces and how to calculate the Figure 27.31 below shows the forces and how to calculate the

torque.torque.

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A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic force on the loop is

Q27.11

A. perpendicular to the plane of the loop, in a direction given by a right-hand rule.

B. perpendicular to the plane of the loop, in a direction given by a left-hand rule.

C. in the same plane as the loop.

D. zero.

E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

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A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic force on the loop is

A27.11

A. perpendicular to the plane of the loop, in a direction given by a right-hand rule.

B. perpendicular to the plane of the loop, in a direction given by a left-hand rule.

C. in the same plane as the loop.

D. zero.

E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

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A. tends to orient the loop so that its plane is perpendicular to the direction of the magnetic field.

B. tends to orient the loop so that its plane is edge-on to the direction of the magnetic field.

C. tends to make the loop rotate around its axis.

D. is zero.

E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic torque on the loop

Q27.12

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A. tends to orient the loop so that its plane is perpendicular to the direction of the magnetic field.

B. tends to orient the loop so that its plane is edge-on to the direction of the magnetic field.

C. tends to make the loop rotate around its axis.

D. is zero.

E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic torque on the loop

A27.12

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• Using the Hall effect we can determine that the charge carriers in conductors Using the Hall effect we can determine that the charge carriers in conductors are negatively charged.are negatively charged.

• For some semiconductors “holes” are the particles!For some semiconductors “holes” are the particles!• This is related to our earlier “mystery”.This is related to our earlier “mystery”.

The Hall EffectThe Hall Effect

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{{Chapter 28Chapter 28

Sources of Magnetic FieldSources of Magnetic Field

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• A moving charge generates a A moving charge generates a magnetic field that depends on magnetic field that depends on the velocity of the charge.the velocity of the charge.

• Figure 28.1 shows the direction Figure 28.1 shows the direction of the fieldof the field..

The magnetic field of a moving charge

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A positive point charge is moving directly toward point P. The magnetic field that the point charge produces at point P

Q28.1

A. points from the charge toward point P.

B. points from point P toward the charge.

C. is perpendicular to the line from the point charge to point P.

D. is zero.

E. The answer depends on the speed of the point charge.

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A positive point charge is moving directly toward point P. The magnetic field that the point charge produces at point P

A28.1

A. points from the charge toward point P.

B. points from point P toward the charge.

C. is perpendicular to the line from the point charge to point P.

D. is zero.

E. The answer depends on the speed of the point charge.

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Q28.2

A. toward the upper point charge (the force is attractive)

B. away from the upper point charge (the force is repulsive)

C. in the direction of the velocity

D. opposite to the direction of the velocity

E. none of the above

Two positive point charges move side by side in the same direction with the same velocity.

What is the direction of the magnetic force that the upper point charge exerts on the lower one?

+q v

+q v

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A28.2

A. toward the upper point charge (the force is attractive)

B. away from the upper point charge (the force is repulsive)

C. in the direction of the velocity

D. opposite to the direction of the velocity

E. none of the above

Two positive point charges move side by side in the same direction with the same velocity.

What is the direction of the magnetic force that the upper point charge exerts on the lower one?

+q v

+q v

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Magnetic field of a current element Magnetic field of a current element • The total magnetic field of

several moving charges is the vector sum of each field.

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Force between parallel conductorsForce between parallel conductors

• The force per unit length on each The force per unit length on each

conductor is conductor is F/L = F/L = 00IIIIL/L/2π2πrr. .

(See Figure 28.9 at the right.)(See Figure 28.9 at the right.)• The conductors attract each other if The conductors attract each other if

the currents are in the same the currents are in the same direction and repel if they are in direction and repel if they are in opposite directions.opposite directions.

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A long straight wire lies along the y-axis and carries current in the positive y-direction.

A positive point charge moves along the x-axis in the positive x-direction. The magnetic force that the wire exerts on the point charge is in

Q28.3

A. the positive x-direction.

B. the negative x-direction.

C. the positive y-direction.

D. the negative y-direction.

E. none of the above

+q

v

x

y

O

I

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A long straight wire lies along the y-axis and carries current in the positive y-direction.

A positive point charge moves along the x-axis in the positive x-direction. The magnetic force that the wire exerts on the point charge is in

A28.3

A. the positive x-direction.

B. the negative x-direction.

C. the positive y-direction.

D. the negative y-direction.

E. none of the above

+q

v

x

y

O

I

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Q28.4

Two long, straight wires are oriented perpendicular to the xy-plane. They carry currents of equal magnitude I in opposite directions as shown. At point P, the magnetic field due to these currents is in

A. the positive x-direction.

B. the negative x-direction.

C. the positive y-direction.

D. the negative y-direction.

E. none of the above

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Two long, straight wires are oriented perpendicular to the xy-plane. They carry currents of equal magnitude I in opposite directions as shown. At point P, the magnetic field due to these currents is in

A28.4

A. the positive x-direction.

B. the negative x-direction.

C. the positive y-direction.

D. the negative y-direction.

E. none of the above