30. Induction and Inductance

An outer ring is connected to a variable voltage source. If the battery's voltage is continuously INCREASING, what is the direction of the induced current in the inner ring, centered inside of the outer ring?

A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of dB/dt = -0.680 T/s. Is the induced current in the loop clockwise or counterclockwise?

The current in Fig. $E29.18$ obeys the equation $I\left(t\right)=I_0{e}^{-bt}$, where $b>0$. Find the direction (clockwise or counterclockwise) of the current induced in the round coil for $t>0$.

A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value B₀. Explain your reasoning.

Using Lenz's law, determine the direction of the current in resistor ab of Fig. E29.19 when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.