Question

A long solenoid with 900 turns/m has a radius of 10.0 cm and carries a current of 0.5 A. This solenoid is 1.2 m long and the wire resistance is R = 2.4 Ω.

a) Reduce the current by a factor of two in 5 μs. What is the direction and magnitude of the electric field at the distance of 5.0 cm away from the axis of solenoid as a function of time?

b) Reduce the current by a factor of two in 5 μs. What is the direction and magnitude of the electric field at the distance of 25.0 cm away from the axis of solenoid as a function of time?

Answer 1

given
number of turns per unit length, n = 900 turns/m
R = 10 cm
I = 0.5 A
L = 1.2 m
Resistance = 2.4 ohms

magnetic field inside the loop, B = mue*n*I

a) at r = 5.0 cm = 0.05 m

induced emf in the imaginary loop = A*dB/dt

E*2*pi*r = pi*r^2*m*n*dI/dt

E = (r/2)*mue*n*dI/dt

= (0.05/2)*4*pi*10^-7*900*(0.5 - 0.25)/(5*10^-6)

= 1.41 N/C <<<<<<<=----------------Answer

direction of E is in the direction of current as solenoid.
b) at r = 25 cm = 0.25 m

induced emf in the imaginary loop = A*dB/dt

E*2*pi*r = pi*R^2*m*n*dI/dt

E = (R^2/(2*r))*mue*n*dI/dt

= (0.1^2/(2*0.25))*4*pi*10^-7*900*(0.5 - 0.25)/(5*10^-6)

= 1.13 N/C <<<<<<<=----------------Answer

direction of E is in the direction of current as solenoid.