a. A conductor in the shape of a square of edge length `l = 0.4 m` carries a current `i=10.0 A`. Calculate the magnitude and direction of magnetic field at the centre of the square.
b. If this conductor is formed into a single circular turn and carries the same current. what is the value of the magnetic field at the centre.

Explanation

a. From screw law, we can see that direction of magnetic field at centre of the square is inwards as the current is clockwise.

`B=4(mu_0/(4pi) i/r)(sinalpha+sinbeta)`
`=(4xx10^-7xx10)/0.2(sin45^@+sin45^@)`
`=2.83xx10^-5T`
b. `2piR=4(0.4)`
`2R=1.6/pim`
`B=(mu_0i)/(2R)=(94pixx10^-7)(10))/((1.6/pi))`
`=24.7xx10^-6T`