A long solenoid carries a current of 30 A . Another coil (of larger diameter tha

Question

A long solenoid carries a current of 30 A . Another coil (of larger diameter than the solenoid) is coaxial with the center of the solenoid, as in the figure. ( Inner coil length is 6m, Outer is 2m. Inner Diameter is 5cm and outer is 15cm.) Find the magnetic field in the solenoid. The outside coil has 250 turns and the inside solenoid has 6400 turns. The permeability of free space is 4 × 107 T · m/A. Answer in units of T. Find the magnetic flux 12 through the crosssectional area of the large circular coil due to the 30 A current in the solenoid. Answer in units of T m2 .Calculate the mutual inductance M of the solenoid and circular coil. Answer in units of H. Assume the current I2 in the solenoid is increasing linearly at a rate of d I2 dt = , where = 9 A/s. What is the magnitude of the voltage E1 across the circular coil? Answer in units of V.

Explanation / Answer

a)

magnetic field inside inner solenoid,

B = mue*N*I/L

= 4*pi*10^-7*6400*30/6

= 4.02*10^-2 T

b) magnetic flux through the outer coil = N2*B*A

= 250*4.02*10^-2*(pi*0.05^2/4)

= 1.973*10^-2 T.m^2

c) mutual inductance, M = magnetic flux/I

= 1.973*10^-2/30

= 6.58*10^-4 H

d) induced emf = M*dI/dt

= 6.58*10^-4*9

= 5.92*10^-3 volts

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