solutions_chapter21

# 2116 set up the magnetic force on a charge in the

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21.16. Set Up: The magnetic force on a charge in the moving bar is given by the right hand rule. The direction of the current is in the direction of this force. Lenz’s law says the field of the induced current opposes the change in flux through the circuit. Solve: (a) The directions of and are shown in Figure 21.16. The magnetic force is toward the top of the bar, so the induced current is from b to a through the bar and counterclockwise in the circuit. Figure 21.16 (b) The magnetic field is into the page and the flux is increasing as the area of the circuit increases. The magnetic field of the induced current therefore is out of the page inside the circuit. To produce a magnetic field in this direction the induced current must be counterclockwise. v B b a F B S v S 1 21-4 Chapter 21

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21.17. Set Up: Use the right-hand rule to find the direction of the magnetic field due to the long wire at the location of each loop. Lenz’s law says that the magnetic field of the induced current is directed to oppose the change in flux through the circuit. Solve: The magnetic field of the long wire is directed out of the page at C and into the page at A. When the current increases, the magnetic field increases. Therefore, the magnetic field of the induced current in loop C is directed into the page inside the loop, to oppose the increase in flux out of the page due to the current in the long wire. To produce magnetic field in this direction, the induced current in C is clockwise. The magnetic field of the induced current in loop A is directed out of the page inside the loop, to oppose the increase in flux into the page due to the current in the long wire. To produce magnetic field in this direction the induced current in A is counterclockwise. Reflect: If the direction of I were reversed the directions of the induced currents would reverse. If I were decreasing rather than increasing, the directions of the induced currents would reverse. 21.18. Set Up: The magnetic field of the bar magnet is directed into the S pole so is toward the top of the page in the figure in the problem. The loop and magnetic field of the bar magnet, as viewed from below the loop, are shown in Figure 21.18. Lenz’s law says that the magnetic field of the induced current is directed to oppose the change in flux through the circuit. Figure 21.18 Solve: (a) The strength of the magnetic field decreases with distance from the coil. When the coil is dropped it moves away from the bar magnet and the flux through the coil decreases and to oppose this decrease the flux due to the induced current is into the page. To produce magnetic field inside the coil that is into the page, the induced cur- rent must be clockwise. (b) When the magnet is dropped, it moves toward the coil and the flux through the coil increases. To oppose this increase, the flux due to the induced current is out of the page. To produce magnetic field inside the coil that is out of the page the induced current must be counterclockwise.

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