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 `54 mu T.` what will be its value at the centre of the loop?

Options

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

Answer

A

Explanation

The magnetic field at a point on the axis of a circular loop at a distance x from the centre is
`B=(mu_(0)//R^(2))/(2(R^(2)+x^(2))^(3//2))`
Given `B=54muT" "x=4cm` " "R=3cm putting the given values in Eq. (i) we get
`54=(mu_(0)Ixx(3)^(2))/(2(3^(2)+4^(2))^(3//2))implies54=(9mu_(0)I)/(2(25)^(3/2))=(9mu_(0)I)/(2xx(5)^(3))`
`:.mu_(0)I=(54xx2xx125)/9impliesmu_(0)I=-1500muT-cm`
Now, putting x = 0 in Eq. (i), magnetic field at the centre of loop is :
`B=(mu_(0)IR^(2))/(2R^(3))=(mu_(0)I)/(2R)=1500/(2xx3)` [From Eq. ii] , `=250 muT`