Q. 57

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Answer :

**Given**

Radius of solenoid is a

Length of the solenoid is l

Number of turns per unit length is n

The current in the circular loop is indx

The magnetic field due to the circular ring at the any distance from the ring is

Where

μ_{o} is the permeability of the free space,

I is the current in the ring

r is the radius of the loop

x is the distance from the loop at which the magnetic field to be found.

Integrating the above equation for x-0 and r

On solving the above equation, we get

The magnetic field at the center of the solenoid due to this circular current

(b) When l≫a

Putting in the equation (i), we get

Putting the values in the above formula, we get

B=μ_{0} n I

When a ≫ l

Putting in the equation (i), we get

Putting the above value in the equation (i), we get

Hence, proved if *l* >> *a*, the field tends to *B* = μ_{0}*ni* and

if *a* >> *l*, the field tends to B, .

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