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Magnetic field of a solenoid

Magnetic field of a solenoid

Physics INK 1 min read
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Find the magnetic field at point P on the axis of a tightly wound solenoid (helical coil) consisting of n turns per unit length wrapped around a cylindrical tube of radius a and carrying current I. Express your answer in terms of 8 and 8. Consider the turns to be essentially circular, and use the result. What is the field on the axis of an infinite solenoid (infinite in both directions)? 

A solenoid is an infinite number of circular loops carrying current . Let us consider a circular loop with no of turn at the distance form the point P. 

The magnetic field due to the circular loop is

Let us express as

or,
or,
and
or
The magnetic field  due to the circular loop becomes,
or,
The magnetic field due to the solenoid is 
or,

For infinite long solenoid:

We have and , The magnetic field becomes,



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