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Find the magnetic field at the centre P ...

Find the magnetic field at the centre `P` of square of side a shown in
.

Text Solution

Verified by Experts

The correct Answer is:
`(2sqrt2-1)(mui)/(pia)`

Field at center may be consider due to superposition of field due to infinite long straight wire `(B_(1))` and field due to square `(B_(2))` Field due to straight wire
`B_(1) = (mu_(0))/(4pi) (2i)/(a//2) = (mu_(0))/(4pi) (4i)/(a) = (mu_(0))/(pia)`
`B_(2)=(4mu_(0))/(4pi) (i)/(a//2) [sin 45^(@) + sin 45^(@)]ox`
`B_(2) = (mu_(0))/(pi) (2sqrt2i)/(a)`
`B = B_(2) -B_(1) = (mu_(0))/(pia) (2 sqrt2v -1) ox`
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