Question

Compare the magnitude of the magnetic field at the center of a circular current loop of radius 50 mm with the magnitude of the magnetic field at the center of a solenoid of the same radius and with 2.0 turn per millimeter. Assume the current is the same through the current loop and the solenoid.

Answer 1

given,

Radius of the circular current = 50 mm

Number of turn = M = 2 turn/mm

magnetic field at the center of the loop

`B = (\mu_0 I)/(2R)`

magnetic field at the center of solenoid

`B' = \mu_o n I`

now, ratio

=
`(B')/(B) = ( \mu_o n I)/((\mu_0 I)/(2R))`

=
`(B')/(B) =2 n R`

=
`(B')/(B) =2* 2 * 50`

B' = 200 B

magnetic field inside the solenoid is 200 times the magnetic field of loop.