The magnetic field B inside a long solenoid, carrying a current of 5.00 A, is `(3.14 xx 10^-2)` T. Find the number of turns per unit length of the solenoid.

Options

A. `K/(2I)`
B. `K/(2 mu_(0)I)`
C. `(mu_(0)K)/(2I)`
D. `K/I`

Answer

a

Explanation

We know that the magnetic field created by thin sheet of current is parallel to the width of strip and for the net magnetic field to become zero at the centre of solenoid the two fields must cancel each other.
Magnetic field near the given large strip of current is denoted as: `B = (mu_(0)K)/2`
If there are n numbers of turns per unit length of the solenoid, then magnetic field at its centre can be written as: `B = mu_(0) nI`
These two fields must be equal and opposite to each other to make the net intensity zero.
` mu_(0) nI = (mu_(0)K)/2 rArr n = K/(2I)`