Physics problem

A small loop of area 8cm^2 is placed inside a long solenoid that has 850 turns/m and carries a sinusoidally varying current given by: i(t)=I₀sin(wt),

 

Where i₀=1.2A is the amplitude and w=200 rad/s is the angular frequency. the central axis of the loop and solenoid coincide (see a cross- section of the solenoid with the the small loop inside in the figure)

 

A) Calc the magnetic field B(t) inside the soldenoid

B) Calc  the total magnetic flux per unit of lenth thru the windings of the solenoid as a function of time

C)Calc th einductance per unit of length of the solenoid

D) Determine th emf induced in the loop