Question

A solenoid used to produce magnetic fields for research purposes is 2.0 m long, with an inner radius of 30 cm and 1000 turns of wire. When running, the solenoid produces a field of 1.0 T in the center. Given this, how large a current does it carry?

Answer 1

The current the solenoid carries is as large as 1591.3 A

Step-by-step explanation:

Given;

length of solenoid, L = 2.0m

radius of the solenoid, R = 30 cm = 0.3 m

number of turns of wire, N = 1000

strength of magnetic field, B = 1.0 T

The magnetic field strength inside a solenoid is;

`B = \mu_o nI\\\\`

Where;

μ₀ is permeability of free space, = 4π x 10⁻⁷

n is number of turns per length

I is the current in the solenoid

`B = \mu_o nI\\\\B = \mu_o (N)/(L) I\\\\B = (\mu_oNI)/(L) \\\\I = (BL)/(\mu_oN) \\\\I = (1*2 )/(4\pi* 10^(-7)*1000) \\\\I = 1591.3 \ A`

Therefore, the current the solenoid carries is as large as 1591.3 A