Q. An air-core solenoid of radius a is made of n turns per unit length. A small loop of wire (radius b) is placed coaxially inside the solenoid. Here b << a.

Part (a): If a current I(t) = I0 cos(!t) is put into the solenoid, use Ampere's Law to determine the expression for the magnetic field strength as a function of time B(t) inside the solenoid.

Part (b): Use Faraday's Law to calculate the induced voltage Vr(t) around the little ring.

Part (c): Calculate the mutual inductance between the little loop and the big solenoid.

Part (d): Suppose the solenoid filled with a paramagnetic substance such as liquid oxygen. Qualitatively,how will this change your your answer to Part (b)? Will your answer increase, decrease,or remain the same?