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….

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)

Sol: 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}}$

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