Question

In the figure, a charged sphere of mass $m$ and charge $q$ starts sliding from rest on a vertical fixed circular track of radius $R$ from the position shown. There exists a uniform and constant horizontal magnetic field of induction $B$ . The maximum force exerted by the track on the sphere is -

• A. $mg$
• B. $3mg- \, qB\sqrt{2 g R}$
• C. $3mg+qB\sqrt{2 g R}$
• D. $mg- \, qB\sqrt{2 g R}$

Answer 1

Answer: (C)

$F_{m}=q \, v \, B$ (directed radially outward)
$\because \, N- \, mg \, sin \theta - \, q \, v \, B=\frac{m v^{2}}{R}$
or $N=\frac{m v^{2}}{R}+mg \, sin \theta +qvB$
$\theta =\pi / 2$
Hence at $\theta =\pi / 2$
$N_{m a x}=\frac{2 m g R}{R}+mg+qB\sqrt{2 g R}$
$=3mg+qB\sqrt{2 g R}$
$N_{m a x}=3mg+qB\sqrt{2 g R}$