Question

A bar magnet of magnetic moment M₁ is cut into two pieces along its axis. The pieces are kept perpendicular to each other with their unlike poles in contact. The magnetic moment of the arrangement is M₂. The ratio of M₁/M₂ is ______.

Options

• `1"/"2sqrt2`

• 1

• `sqrt2`

• `1"/"sqrt2`

Answer 1

A bar magnet of magnetic moment M₁ is cut into two pieces along its axis. The pieces are kept perpendicular to each other with their unlike poles in contact. The magnetic moment of the arrangement is M₂. The ratio of M₁/M₂ is `underlinebb(sqrt2)`.

Explanation:

In the given case, the magnetic moment of the pieces gets halved.

i.e., `M_1^' = M_2^' = M_1/2`

The magnetic moment of the given arrangement,

`M_2 = sqrt((M_1^')^2 + (M_2^')^2`

= `sqrt((M_1/2)^2 + (M_1/2)^2) = M_1/sqrt2`

⇒ `M_1/M_2 = sqrt2`