A long straight ideal solenoid of radius 6 cm, with 150 turns/m passes (on axis)

Question

A long straight ideal solenoid of radius 6 cm, with 150 turns/m passes (on axis) through the center of a flat circular coil, of radius 9 cm, with 15 turns. The current in the solenoid varies with time as I(t) = 4sin(3t) A counterclockwise.

a. What is the total flux across the coil, as a function of time?

b.   What is the induced emf in the coil as a function of time?

c.   The wire of the coil has cross-sectional area of 30 mm2. At t = 0, electromechanical energy is being converted to thermal energy in the coil at a rate of 4 W. What is the resistivity, %u03C1, of the coil material?

d. What is the magnitude of the electric field inside the wire of the coil at t=0?         

Explanation / Answer

B=(permeability of free space)(Number of turns/Length)Current

=4*pi*10^-7*150*4sin3t=0.00075sin3t

flux=BA=8.52*10^-6sin3t

induced emf=ndf/dt=3.83*10^-4cos3t

c)at t=0 emf=3.83*10^-4V

resistance = V^2/P=(3.83*10^-4)^2/4=3.66*10^-8ohm

R=pL/A

3.66*10^-8=15*2*pi*0.09*p/(30*10^-6)

or p = 1.3*10^-13ohm m

Electric field = V/l=3.83*10^-4/(15*2*pi*0.09)=4.5*10^-5 V/m

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