The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is

Question

The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is (A) 2-3 (B) 2-1 / 3 (C) 23 (D) 21 / 3

Tardigrade Admin · Accepted Answer

B1=(2 M/x3) and B2=(M/y3) As B1=B2 Hence (2 M/x3)=(M/y3) or (x3/y3)=2 or (x/y)=21 / 3

Q. The magnetic field at a point $x$ on the axis of a small bar magnet is equal to the field at a point $y$ on the equator of the same magnet. The ratio of the distances of $x$ and $y$ from the centre of the magnet is

$2^{- 3}$

$2^{- 1/3}$

$2^{3}$

$2^{1/3}$

$B_{1} = \frac{2 M}{x ^{3}}$ and $B_{2} = \frac{M}{y ^{3}}$
As $B_{1} = B_{2}$
Hence $\frac{2 M}{x ^{3}} = \frac{M}{y ^{3}}$
or $\frac{x ^{3}}{y ^{3}} = 2$ or $\frac{x}{y} = 2^{1/3}$

Q. The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is

2−3

2−1/3

23

21/3