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

Options

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

Answer

D

Explanation

`B_("axis") =(mu_(0))/(4pi )[(2piI r ^(2))/((r^(2) +x^(2))^(3//2))]`
`B_("centre")=(mu_(0))/(4pi)[(2piI)/(r)]`
`therefore (B_(C))/(B_(A))=((r^(2)+x^(2)))/(r ^(3))but r =3 and x=4 cm `
`therefore (B_(C))/(B_(A)) =((5 ^(2))^(3//2))/(3 ^(3))=(125)/(27) `
`therefore B_(C) =(125)/(27) B_(A)=(125)/(27) xx54 =250 mu T`