© 2012 Pearson Education, Inc. { Chapter 27 Magnetic Fields and Forces (cont.)

© 2012 Pearson Education, Inc. Force and torque on a current loop 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. 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. Figure below shows the forces and how to calculate the torque. Figure below shows the forces and how to calculate the torque.

© 2012 Pearson Education, Inc. 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.

© 2012 Pearson Education, Inc. 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.

© 2012 Pearson Education, Inc. 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

© 2012 Pearson Education, Inc. 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

© 2012 Pearson Education, Inc. Using the Hall effect we can determine that the charge carriers in conductors are negatively charged. Using the Hall effect we can determine that the charge carriers in conductors 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 Effect

© 2012 Pearson Education, Inc. { Chapter 28 Sources of Magnetic Field

© 2012 Pearson Education, Inc. A moving charge generates a magnetic field that depends on the velocity of the charge. A moving charge generates a magnetic field that depends on the velocity of the charge. Figure 28.1 shows the direction of the field. Figure 28.1 shows the direction of the field. The magnetic field of a moving charge

© 2012 Pearson Education, Inc. 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.

© 2012 Pearson Education, Inc. 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.

© 2012 Pearson Education, Inc. 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+q +q+q

© 2012 Pearson Education, Inc. 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+q +q+q

© 2012 Pearson Education, Inc. Magnetic field of a current element The total magnetic field of several moving charges is the vector sum of each field.

© 2012 Pearson Education, Inc. Force between parallel conductors The force per unit length on each conductor is F/L =  0 IIL/2πr. (See Figure 28.9 at the right.) The force per unit length on each conductor is F/L =  0 IIL/2πr. (See Figure 28.9 at the right.) The conductors attract each other if the currents are in the same direction and repel if they are in opposite directions. The conductors attract each other if the currents are in the same direction and repel if they are in opposite directions.

© 2012 Pearson Education, Inc. 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+q x y O I

© 2012 Pearson Education, Inc. 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+q x y O I

© 2012 Pearson Education, Inc. 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

© 2012 Pearson Education, Inc. 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