A square wire of each side l carries a current I. What is the magnetic field at the midpoint of the square ?

Options

A. `4 sqrt(2) (mu_(o))/(4 pi) (l)/(I)`
B. `8 sqrt(2) (mu_(o))/(4 pi) (l)/(I)`
C. `16 sqrt(2) (mu_(o))/(4 pi) (l)/(I)`
D. `32 sqrt(2) (mu_(o))/(4 pi) (l)/(I)`

Answer

B

Explanation

`B = B_(1) + B_(2) + B_(3) + B_(4)" "B = 4[(mu_(0))/(4 pi).(l)/(a) (sin theta_(1) + sin theta_(2))]`
`B = 4 xx (mu_(0))/(4 pi) (l)/((l//2)) [(1)/(sqrt(2)) + (1)/(sqrt(2))]`
Here, `a = (l)/(2), theta_(1) = theta_(2) = 45^(@)`
`therefore" "B = (16)/(sqrt(2)) [(mu_(0))/(4 pi)(l)/(l)] = 8 sqrt(2) ((mu_(0))/(4 pi) (l)/(l))`