A current of` 2*00 A` exists in a square loop of edge `10*0 cm`. Find the magnetic field B at the centre of the square loop.

Explanation

Solution: The magnetic fields at the centre due to the four
sides will be equal in magnitude and direction. The field
due to one side will be
` B_1 = (mu_0)ia/ 2 pi d (sqrt (a^2 + 4 d^2))`
` Here, a= 10cm and d= a/2= 5cm.`
Thus,
` B_1= ((mu_0)(2A)/(2pi(5cm))) [(10cm)/(sqrt(10 cm^2) + (4 (5 cm)^2))]`
` = 2 xx (10^-7) TmA^-1 xx 2A xx (1/5 (sqrt(2cm)))`
` = 5*66 xx (10^-6) T.`
Hence, the net field at the centre of the loop will be
` 4 xx 5*66 xx (10^-6) T= 22*6 xx (10^-6) T .