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

Options

A. `250muT`
B. `150muT`
C. `125muT`
D. `75muT`

Answer

4

Explanation

The magnetic field at a point on the axis of a circular loop at distance x from the center is
`B =(mu_(0)iR^(2))/(2(R^(2) + x^(2))^(3//2))`
Given `% B = 54 mu T, x =4 cm, R =3cm`
Putting the given values we get
`:. 54 =(mu_(0)ixx(3)^(2))/(2(3^(2)+4^(2))^(3//2))`
`implies 54 = (9mu_(0)i)/(2(25)^(3//2)) (9mu_(0)i)/(2xx(5)^(3))`
`:. mu_(0)i =(54 xx2 xx 125)/(9)`
`mu_(0) i =1500`
Now, putting `x = 0` in equation (i) magnetic field at the centre of loop is
`B = (mu_(0)iR^(2))/(2xx3) = (mu_(0)i)/(2R)`
` =(1500)/(2 xx3) =250 muT` .