In two separate experiments, the neutral points due to two small magnets are at a distance of r and 2 r in broad side-on position. The ratio of their magnetic moments will be

Question

In two separate experiments, the neutral points due to two small magnets are at a distance of r and 2 r in broad side-on position. The ratio of their magnetic moments will be (A) 4: 1 (B) 1: 2 (C) 2: 1 (D) 1: 8

Tardigrade Admin · Accepted Answer

At broad side-on position, B=(M/d3) ∴ (M1/d13)=(M2/d23) or (M1/r3)=(M2/8 r3) or (M1/M2)=(r3/8 r3)=(1/8)

Q. In two separate experiments, the neutral points due to two small magnets are at a distance of $r$ and $2 r$ in broad side-on position. The ratio of their magnetic moments will be

4 : 1

1 : 2

2 : 1

1 : 8

At broad side-on position, $B = \frac{M}{d ^{3}}$
$∴ \frac{M _{1}}{d _{1}^{3}} = \frac{M _{2}}{d _{2}^{3}}$
or $\frac{M _{1}}{r ^{3}} = \frac{M _{2}}{8 r ^{3}}$
or $\frac{M _{1}}{M _{2}} = \frac{r ^{3}}{8 r ^{3}} = \frac{1}{8}$

Q. In two separate experiments, the neutral points due to two small magnets are at a distance of r and 2r in broad side-on position. The ratio of their magnetic moments will be