13.4 Induced Electric Fields

Suppose that the coil of the reference is a square rather than circular. Can the equation be used to calculate (a) the induced emf and (b) the induced electric field?

What is the magnitude of the induced electric field in the example at $t = 0$ if $r = 6.0 \text{cm} ,$ $R = 2.0 \text{cm} , n = 2000$ turns per meter, $I_{0} = 2.0 \text{A} ,$ and $\alpha = 200 \text{s}^{− 1} ?$

Is the work required to accelerate a rod from rest to a speed v in a magnetic field greater than the final kinetic energy of the rod? Why?

Calculate the induced electric field in a 50-turn coil with a diameter of 15 cm that is placed in a spatially uniform magnetic field of magnitude 0.50 T so that the face of the coil and the magnetic field are perpendicular. This magnetic field is reduced to zero in 0.10 seconds. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil.

The current I through a long solenoid with n turns per meter and radius R is changing with time as given by dI/dt. Calculate the induced electric field as a function of distance r from the central axis of the solenoid.

The current in a long solenoid with 20 turns per centimeter of radius 3 cm is varied with time at a rate of 2 A/s. A circular loop of wire of radius 5 cm and resistance $2 \Omega$ surrounds the solenoid. Find the electrical current induced in the loop.