The maganetic field due to a current carryion circular loop of radius 3cm at a point on the axis at a distance of 4m from the centre is 54 `mu`T. what will be its value at the centre of the loop?

Options

A. 250`mu`T
B. 150`mu`T
C. 125`mu`T
D. 75`mu`T

Answer

A

Explanation

Field along axis of coil, `B=(mu_(0)lR^(2))/(2(R^(2)+x^(2))^(3"/"2))`
At the centre of coil `B=(mu_(0)l)/(2R)`
`:.(B^(.))/(B)=(mu_(0)l)/(2R)xx(2(R^(2)+x^(2)))/(mu_(0)IR^(2))=((R^(2)+x^(2))^(3"/"2))/(R^(3))`
`:. B^(.)=(Bxx(R^(2)+x^(2)))^(3"/"2)/(R^(3))=(54xx[(3)^(2)+(4)^(2)]^(3"/"2))/((3^(3)))=(54xx125)/(27)`
`or B^(.)=250mu_(0)T`