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 -

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F m = q v B (directed radially outward) ∵ N - m g sin ⁡ θ - q v B = m v 2 R or N = m v 2 R + m g sin ⁡ θ + q v B θ = π / 2 Hence at θ = π / 2 N m a x = 2 m g R R + m g + q B 2 g R = 3 m g + q B 2 g R N m a x = 3 m g + q B 2 g R

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