Question

A negatively charged body of charge -Q and mass M slides down the inner curved surface of a frictionless hemispherical vessel from a point P. Throughout the motion, the region is filled with a constant magnetic induction B, directed perpendicularly to the plane containing the motion. Determine the magnitude of the contact force exerted by the surface on the body when it passes a position N on the curve.

• A. mgsinθ + qB√(2gRsinθ)
• B. 3mgsinθ + qB√(2gRsinθ)
• C. mgsinθ - qB√(2gRsinθ)
• D. 3mgsinθ - qB√(2gRsinθ)

Answer 1

Answer: (D)

3mgsinθ - qB√(2gRsinθ)

Answer 2

Assuming $\theta$ is the angle from the horizontal and the magnetic force is directed outwards, the radial equation is $N - mg\sin\theta + F_B = Mv^2/R$. With $v^2 = 2gR\sin\theta$, this leads to $N = 3Mg\sin\theta - QB\sqrt{2gR\sin\theta}$.