Q. A magnet of length 2L and moment ‘M’ is axially cut into two equal halves ‘P’ and ‘Q’. The piece ‘P’ is bent in the form of semi circle and ‘Q’ is attached to it as shown. Its moment is
(a) $ \displaystyle \frac{M}{\pi}$
(b) $ \displaystyle \frac{M}{2 \pi}$
(c) $ \displaystyle \frac{M(2+\pi)}{2\pi}$
(d) $ \displaystyle \frac{M \pi}{2+\pi}$
Ans:(c)
Sol: For Part P ;
$ \displaystyle M_P = m \times 2R $
$ \displaystyle M_P = m \times 2 \times \frac{L}{\pi} $
$ \displaystyle M_P = \frac{M}{\pi} $
For Part Q ,
$ \displaystyle M_Q = \frac{M}{2} $
Both the magnetic moment have same direction ;
Hence net magnetic moment is
$ \displaystyle M_R = M_P + M_Q $
$ \displaystyle M_R =\frac{M}{\pi} + \frac{M}{2} $