(II) If the solenoid in Fig. 29–47 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

At a given instant, a 2.4-A current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1.60 cm on a side?

(III) A toroid has a rectangular cross section as shown in Fig. 30–26. Show that the self-inductance is

$L=\frac{{\mu }_0{N}^{2}h}{2\pi }\ln \frac{r_2}{r_1}$

where N is the total number of turns and r₁, r₂ and h are the dimensions shown in Fig. 30–26. [Hint: Use Ampère’s law to get B as a function of r inside the toroid, and integrate.]

A coil has 3.25-Ω resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.15 A/s, what is the potential difference across the coil at this moment?

(III) A long straight wire and a small rectangular wire loop lie in the same plane, Fig. 30–25. Determine the mutual inductance in terms of 𝓁₁, 𝓁₂, and w. Assume the wire is very long compared to 𝓁₁, 𝓁₂, and w, and that the rest of its circuit is very far away compared to 𝓁₁, 𝓁₂, and w.

(II) Part of a single rectangular loop of wire with dimensions shown in Fig. 29–49 is situated inside a region of uniform magnetic field of 0.650 T. The total resistance of the loop is 0.250 Ω. Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.40 m/s. Neglect gravity.