Question

1. A toroidal coil is centered at the origin as picture with current wrapping around as pictured. There is no current running in the phi-hat direction. The current, I, is increasing in time. What is the direction of the E field at the origin? a. + d. -y b. -X e. +z c. ty f. -Z 2. Which of Maxwell's equations can be used to find the continuity equation? (with the proper use of curl or divergence) please choose equation and state curl or divergence a. Gauss's law for E fields C. Faraday's law b. Gauss's law for B fields d. Ampere/Maxwell law a. Divergence b. Curl 3. A metal wire is resting on a U-shaped conducting rail. The rail is fixed and x x x x the magnetic field is shown going into the page. What will happen to the wire if the magnetic field increases? x x x x a. Remain in place d. Rotate CW b. Move to the right e. Rotate CCW |x x x x C. Move to the left f. Slide vertically off the rails x x xx

Answer 1

1) The magnetic field due to a toroid inside is given by

B= HON7 271

So, the magnetic field is proportional to the current.

The field will be in the direction of current Si, here, the field is in the +z direction

As current increases, magnetic field increases. This increase in magnetic field will induce an electric field

Since the emf generated is in the opposite direction to the change in magnetic field according to faraday's law,

E will be in the -Z direction. Option F

2) The continuity equation can be obtained by taking divergence on both sides of the ampere's law.

V. +) = V. (V x H) = 0

[A-= (a Ale

V.J= Opi

So, the answer is

Option D and Option A

3) Here, initially, the metal wire is not moving. A change in magnetic field will induce a current through the circuit. Thus electrons in the metal will start moving in the counter- clock wise direction.

So, the electrons in the wire will start moving upward (the rod is still stationary.)

Now, due to the motion of charge, a force is there in the coil in the direction of vXB

B, into the plane and v upward.

So, the force will be to the right. This will cause the metal rod to move to the right.

Option B