A square conducting loop of side length L carries a current I.The magnetic field at the centre of the loop is (dependence on L)

Options

A. independent of `L`
B. proportional to `L_(2)`
C. inversely proportional to `L`
D. inversely proportional to `L`

Answer

C

Explanation

Magnetic field at the centre due to either arm
`B_(1)=(mu_(0))/(4pi)xx1/((L//2))[sin45^(@)+sin45^(@)]`
`=(mu_(0))/(4pi)=(2sqrt(2I))/L`
Field at centre due to the four arms of the square
`B=4B_(1)=(mu_(0))/(4pi)xx(2sqrt(2I))/L`
i.e., `B prop1/L`