JEE Main | 2018Magnetic field due to currentHard

Question

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B2. The ratio B1B2 is :

Options

A.

3

B.

2

C.

12

D.

2

Solution

Dipole moment of circular loop is m
m1 = I.A = I.πR2 {R = radius of the loop}
B1 = μ0I2R
moment becomes double
⇒R becomes 2R (keeping current
constant)
m2 = I. π(2R)2 = 2.IπR2 = 2m1
B2 = =μ0I2(2R)=B12
B1B2=2

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