Question

Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1. The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is:___________A. 2B. 4C. 6D. 1E. 1/3

Answer 1

Given :

Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1.

To Find :

The ratio of the magnetic field in the interior of 2 to that in the interior of 1.

Solution :

We know, magnetic field in the interior of a solenoid is given by :

`B = (\mu ni)/(L)`

Let, length of solenoid 2 is L.

Therefore, length of solenoid 1 is 6L.

`B_a=(\mu (6n)i)/(L)\\\\B_b = (\mu n i)/(L)`

Dividing
`B_a` by
`B_b` :

`(B_a)/(B_b)=((\mu (6n)i)/(L))/((\mu n i)/(L))\\\\(B_a)/(B_b)=6`

Therefore, the correct answer is C. 6.