IIT JEE , AIEEE Forum - Physics , Magnetism - Mind-Storming by Mr.IITIAN007

Mr.IITIAN007

A wire of length L carrying an electric current i , is bent in the form of a polygon of number of sides=n .Then what is the magnetic field induction at the centre of the polygon ?

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Q) A wire of length L carrying an electric current i , is bent in the form of a polygon of number of sides=n .Then what is the magnetic field induction at the centre of the polygon ?

Solution) The approach to solve this problem is as follows:

Use Biot-Savart's law.

Here since the magnetic induction due all sides of polygon will be same.

so just find magnetic induction at center due to any one side of the polygon = B (let)

then magnetic induction at the center due to polygon = nB

here length of one side AB = L/n.

If center of the polygon be 'C'

then angle between between CA and AB = 180/n

similarly angle b/w CB and AB = 180/n

Now biot savart's law is = dB =

o i x dl / r ²

where r = distance of element dl (through which current i is flowing ) from center C.

now integrate this expression between the two limits to find B due to side AB of the polygon.

Now total magnetic field will be = nB

Mr.IITIAN007

Thanks for the solution.

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