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 induction $B$. The maximum force exerted by the track on the sphere is :

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

Answer 1

The correct option is B $3mg-qB\sqrt{2gR}$

$F_m=qvB,$ and directed radially outward$.$

$\because N-mg\sin \theta +qvB=\frac{m{v}^2}{R}$

$\Rightarrow N=\frac{m{v}^2}{R}+mg\sin \theta -qvB$

Hence at $\theta =\frac{\pi }{2}$

$\Rightarrow N_{max}=\frac{2mgR}{R}+mg-qB\sqrt{2gR}$

$=3mg-qB\sqrt{2gR}$

Hence,

option $\left(B\right)$ is correct answer.