A wire in the form of a square of side a carries a current I Then, the magnetic induction at the centre of the square is (magnetic permeability of free space= `mu_(0)`)

Options

A. `(mu_(0)i)/(2pia)`
B. `(mu_(0)isqrt2)/(pia)`
C. `(2sqrt2mu_(0)i)/(pia)`
D. `(mu_(0)i)/(sqrt2pia`

Answer

C

Explanation

`alpha=beta=45^(@),R=a/2`
`=(mu_(0)i)/(4pixxa/2)("cos"45^(@)+"cos"45^(@))``=(2mu_(0)i)/(4pia)(1/sqrt2+1/sqrt2)=(2sqrt2mu_(0)i)/(4pia)` Total magnetic field at the centre,
`B=4B_(1)=4((2sqrt2mu_(0)i)/(4pia))=(2srt2mu_(0)i)/(pia)`