Question

An engineer proposes to store 50 kJ of energy by flowing 1.5 kA of current through a superconducting solenoid that forms an inductor.

Part A
What is the required inductance L?
Express your answer to two significant figures and include appropriate units.

Part B
If the solenoid is to have a radius of 1.2 m and be wound with no more than 5 turns per meter, what length must the solenoid have?
Express your answer to two significant figures and include appropriate units.

Answer 1

Here ,

energy = 50 kJ = 50000 J

current , I = 1.5 kA = 1500 A

part A) let the required inductance is L

Energy = 0.50 LI^2

50000 = 0.50 * L * 1500^2

solving for L

L = 0.044 H

the required inductance is 0.044 H

part B)

let the length is l

for the coils is N = 5 turns/m

Inductance = u0 * (N * l)^2 * Area/l

0.044 = 4pi *10^-7 *(5 * l)^2 * pi * 1.2^2/l

solving for l

l = 309 m
the length of the coil is 309 m