Question

Question text

Consider a long solenoid of length = 1m, radius = 3.0 cm and 800 turns/m. If the rate of change of current is 40 A/s what voltage is induced?

Select one:

a. 11 mV

b. 0.6 mV

c. 91 mV

d. 70 mV

e. 0.4 mV

Answer 1

Magnetic field in the solenoid, B = _o * n * I
Where _o is the vacuum permeability, n is the number of turns per unit length and I is the current

Magnetic flux, = N * B * A
Where n is the number of turns and A is the area.
N = n * L, where L is the length of the solenoid.
N = 800 * 1 = 800
A = R², wher R is the radius of the solenoid.

= N * [_o * n * I] * R²
Voltage induced, V = d/dt
= N * [_o * n * dI/dt] * R²
Substituting values,
V = 800 * [4 * 10^-7 * 800 * 40] * [ * (3 * 10^-2)²]
= 800 * [4.02 * 10^-2] * [2.83 * 10^-3]
= 90.96 * 10^-3 V
= 91 mV