3) A long conducting cylinder with inner radius a= 2.0 cm and outer radius b = 5.0 cm. The cylinder carries a current out of the page, and the current density in the cross section is given by , with and r in meters. What is the magnetic field at a point that is 3.0 cm from the central axis of the cylinder?

4) A small coil of N turns has its plane perpendicular to a uniform magnetic field as shown in the figure below. The coil is connected to a current integrator ©, a device designed to measure the total charge passing through it. (a) Find the total charge passing through the coil if the coil is rotated through about its diameter. (b) Express the magnetic field B in terms of the total charge Q. Hint: You should be able to express your answer in terms of the total flux change.

a)

b)

BONUS PROBLEM: 10 pts

5) A rectangular loop of wire with length a, width b, and resistance R is placed near an infinitely long wire carrying current I, as shown in the figure below. The distance from the long wire to the center of the loop is r. Find (a) The magnitude of the magnetic flux through the loop and (b) the current in the loop as it moves away from the wire with speed v.

a)

is into the page, and where is out of the page.

b) Let r=vt. Then