Question

Suppose you have a 34.9 m length of copper wire. If the wire is wrapped into a solenoid 0.240 m long and having a radius of 0.0510 m, how strong is the resulting magnetic field in its center when the current is 11.0 A?

Answer 1

the strength of the magnetic field inside the solenoid is 6.278 x 10⁻³ T.

Step-by-step explanation:

Given;

length of the wire, = 34.9 m

length of solenoid, L = 0.24 m

radius of the solenoid, r = 0.051 m

current in the solenoid, I = 11.0 A

The number of turns of the wire is calculated as follow;

`N = (34.9)/(2\pi * 0.051) = 109 \ turns`

The strength of the magnetic field inside the solenoid is calculated as follows;

`B = \mu_0 ((N)/(L) )I\\\\B = 4\pi * 10^(-7) * ((109)/(0.24) )* 11.0 \\\\B = 6.278 * 10^(-3) \ T`

Therefore, the strength of the magnetic field inside the solenoid is 6.278 x 10⁻³ T.