Based on the results of Problem 88, the U.S. Navy has developed ways to make the magneti...

Based on the results of Problem 88, the U.S. Navy has developed ways to make the magnetic field from its own submarines as small as possible. One way is by wrapping a solenoid around the hull and passing a current through the solenoid so that the field produced by the solenoid approximately cancels the field from the hull. Take the diameter of the submarine to be 20 m and its length to be 50 m. Assume the field of the submarine alone to be 0.0010 T. Assuming a solenoid with 1000 turns, what is the approximate current required in the solenoid?

(reference problem 88)

The U.S. Navy can detect a submarine by measuring the magnetic field produced by its metal hull (usually made of a magnetic metal). For the purpose of calculating its magnetic field, model a submarine as one large current loop located at the middle of the submarine carrying 8000 A, as calculated in Example 20.9 and with a diameter equal to the diameter of the submarine. Assume that far from the submarine the magnitude of the magnetic field varies as where is the field at the center of the current loop, is the radius of the loop, and r is the distance from the center of the loop (and also the center of the submarine). What is the approximate value of the magnetic field a distance of 1000 m from the submarine?

(reference example 20.9)