The magnetic field at the centre of a current carrying circular loop of radius R is 16 μT

Q. The magnetic field at the centre of a current carrying circular loop of radius R is 16 μT.

The magnetic field at a distance x = √3 R on its axis from the centre is ______ μT.

(A) 8

(B) 2

(C) 4

Correct Answer: 2

Explanation

The magnetic field at the centre of a circular current carrying loop of radius R is:

Bcentre = μ0I / (2R)

The magnetic field on the axis of the loop at a distance x from the centre is given by:

B = (μ0I R2) / [2 (R2 + x2)3/2]

Taking ratio of magnetic field at distance x to that at the centre:

B / Bcentre = R3 / (R2 + x2)3/2

Given x = √3 R,

R2 + x2 = R2 + 3R2 = 4R2

(R2 + x2)3/2 = (4R2)3/2 = 8R3

Therefore,

B = Bcentre × (R3 / 8R3) = 16 × 1/8

B = 2 μT

Hence, the magnetic field at the given point is:

2 μT

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