The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is `54muT`. What will be its value at the centre of the loop ?

Explanation

Magnetic field on the axis of a circular conductor, `B=(mu_(0)I)/(2)(r^(2))/((r^(2)+x^(2))^(3//2))` and magnetic field at the centre `(x=0)` is,
`B'=(mu_(0)I)/(2r)`
`:. (B')/(B)=((r^(2)+x^(2))^(3//2))/(r^(3))`
or, `B'=((r^(2)+x^(2))^(3//2))/(r^(3))B`
`=((3^(2)+4^(2))^(3//2))/(3^(3))xx54`
`:. B' =250muT`