An infinitely long wire carrying a 30 A current in the negative x direction is placed along the x axis near a 40-turn circular loop located in the x-y plane as shown below. If the magnetic field at the center of the loop is zero, what is the direction and magnitude of the current flowing in the loop? 2 m a) 0.24 A, counter clockwise b) 0.24 A, clockwise c) 1.44 A, counter clockwise d) 1.44 A, clockwise e) 0.72 A, clockwise d = 2m

The current in a long solenoid of radius 3 cm and 20 turns cm is varied with time at a rate of 2 A/s. Find the electric field at a distance of 4 cm from die center of the solenoid.

A very long, cylindrical wire of radius a has a circular hole of radius b in it at a distance d from the center. The wire carries a uniform current of magnitude I through it. The direction of the current in the figure is out of the paper. Find the magnetic field (a) at a point at the edge of the hole closest to the center of the thick wire, (b) at an arbitrary point inside the hole, and (c) at an arbitrary point outside the wire. (Hint: Think of the hole as a sum of two wires carrying current in the opposite directions.)

Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)