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 (B1/B2) is :

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 (B1/B2) is : (A) 2 (B) √3 (C) √2 (D) (1/√2)

Tardigrade Admin · Accepted Answer

m=I(π R2), m'=2 m=I ×(π √2 R)2 ∴ R'=√2 R B1=(μ0 I/2 R) B2=(μ0 I/2 ×(√2 R)) ∴ (B1/B2)=√2

Q. The dipole moment of a circular loop carrying a current $I$ , is $m$ and the magnetic field at the centre of the loop is $B_{1}$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$ . The ratio $\frac{B _{1}}{B _{2}}$ is :

$2$

$3$

$2$

$\frac{1}{2}$

$m = I (π R^{2}), m^{'} = 2 m = I \times (π 2 R)^{2}$
$∴ R^{'} = 2 R$
$B_{1} = \frac{μ _{0} I}{2 R}$
$B_{2} = \frac{μ _{0} I}{2 \times ( 2 R )}$
$∴ \frac{B _{1}}{B _{2}} = 2$

Q. 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 B2​B1​​ is :

2

3​

2​

2​1​

m=I(πR2),m′=2m=I×(π2​R)2 ∴R′=2​R B1​=2Rμ0​I​ B2​=2×(2​R)μ0​I​ ∴B2​B1​​=2​

Q. The dipole moment of a circular loop carrying a current $I$ , is $m$ and the magnetic field at the centre of the loop is $B_{1}$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$ . The ratio $\frac{B _{1}}{B _{2}}$ is :

$2$

$3$

$2$

$\frac{1}{2}$

$m = I (π R^{2}), m^{'} = 2 m = I \times (π 2 R)^{2}$
$∴ R^{'} = 2 R$
$B_{1} = \frac{μ _{0} I}{2 R}$
$B_{2} = \frac{μ _{0} I}{2 \times ( 2 R )}$
$∴ \frac{B _{1}}{B _{2}} = 2$