Q. A thin bar magnet of length ‘*l*’ and magnetic moment ‘M’ is bent at the mid point so that the two parts are at right angles. The new magnetic length and magnetic moment are respectively

(a) √2l , √2M

(b) l/√2 , M/√2

(c) √2l , M /√2

(d) l/√2 , √2M

Ans: (b)

Solution : Net magnetic moment

$\displaystyle M_R = \sqrt{(\frac{M}{2})^2 + (\frac{M}{2})^2} $

$ \displaystyle M_R = \sqrt{\frac{M^2}{2}} = \frac{M}{\sqrt{2}}$

Effective length $\displaystyle = \sqrt{(\frac{l}{2})^2 + (\frac{l}{2})^2} $

$ \displaystyle = \sqrt{\frac{l^2}{2}} = \frac{l}{\sqrt{2}}$