1. Active Figure 31.1 (a) When a magnet is moved toward a loop of wire connected to a sensitive ammeter, the ammeter deflects as shown, indicating that a current is induced in the loop. (b) When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop. (c) When the magnet is moved away from the loop, the ammeter deflects in the opposite direction, indicating that the induced current is opposite that shown in part (a). Changing the direction of the magnet’s motion changes the direction of the current induced by that motion.

2. Figure The magnetic flux through an area element dAis BdA BdAcos θ, where dA is a vector perpendicular to the surface.

3. Active Figure Magnetic flux through a plane lying in a magnetic field. (a) The flux through the plane is zero when the magnetic field is parallel to the plane surface. (b) The flux through the plane is a maximum when the magnetic field is perpendicular to the plane.

4. Figure 31.3 A conducting loop that encloses an area A in the presence of a uniform magnetic field B. The angle between B and the normal to the loop is .

5. Figure 31.9 A straight electrical conductor of length moving with a velocity v through a uniform magnetic field B directed perpendicular to v. Due to the magnetic force on electrons, the ends of the conductor become oppositely charged. This establishes an electric field in the conductor. In steady state, the electric and magnetic forces on an electron in the wire are balanced.

6. Active Figure (a) A conducting bar sliding with a velocity v along two conducting rails under the action of an applied force Fapp. The magnetic force FB opposes the motion, and a counterclockwise current I is induced in the loop. (b) The equivalent circuit diagram for the setup shown in part (a).

7. Active Figure 31. 21 (a) Schematic diagram of an AC generator
Active Figure (a) Schematic diagram of an AC generator. An emf is induced in a loop that rotates in a magnetic field. (b) The alternating emf induced in the loop plotted as a function of time.

8. Figure (a) As the conducting bar slides on the two fixed conducting rails, the magnetic flux due to the external magnetic field into the page through the area enclosed by the loop increases in time. By Lenz’s law, the induced current must be counterclockwise so as to produce a counteracting magnetic field directed out of the page. (b) When the bar moves to the left, the induced current must be clockwise. Why?

9. Figure (a) When the magnet is moved toward the stationary conducting loop, a current is induced in the direction shown. (b) This induced current produces its own magnetic field directed to the left that counteracts the increasing external flux. (c) When the magnet is moved away from the stationary conducting loop, a current is induced in the direction shown. (d) This induced current produces a magnetic field directed to the right and so counteracts the decreasing external flux.

10. Figure A conducting loop of radius r in a uniform magnetic field perpendicular to the plane of the loop. If B changes in time, an electric field is induced in a direction tangent to the circumference of the loop.

11. Figure 32.1 After the switch is closed, the current produces a magnetic flux through the area enclosed by the loop. As the current increases toward its equilibrium value, this magnetic flux changes in time and induces an emf in the loop.

12. Active Figure 32. 3 A series RL circuit
Active Figure 32.3 A series RL circuit. As the current increases toward its maximum value, an emf that opposes the increasing current is induced in the inductor.

13. Active Figure 32.4 Plot of the current versus time for the RL circuit shown in Figure The switch is open for t= 0 and then closed at t < 0, and the current increases toward its maximum value /R. The time constant is the time interval required for I to reach 63.2% of its maximum value.

14. Figure 32.5 Plot of dI/dt versus time for the RL circuit shown in Figure The time rate of change of current is a maximum at t 0, which is the instant at which the switch is closed. The rate decreases exponentially with time as I increases toward its maximum value.

15. Active Figure 32. 6 An RL circuit
Active Figure 32.6 An RL circuit. When the switch S is in position a, the battery is in the circuit. When the switch is thrown to position b, the battery is no longer part of the circuit. The switch is designed so that it is never open, which would cause the current to stop.

16. Active Figure 32.7 Current versus time for the right-hand loop of the circuit shown in Figure For t < 0, the switch S is at position a. At t = 0, the switch is thrown to position b, and the current has its maximum value /R.