Two smooth conducting rails are fixed vertically 0.60m apart and joined at the top by a conducting bar of negligible resistance. A metal rod of mass 0.20kg and resistance 0.50Ω can slide without friction down the rails, which are inclined at an angle 30∘ to the horizontal. The entire arrangement lies in a uniform magnetic field of magnitude 0.80T directed horizontally and perpendicular to the plane of the rails. The resistance of the rails and connecting leads is negligible.
(i) Show that as the rod slides it experiences a magnetic force opposing its motion and write this force in terms of the current I in the rod.
(ii) Obtain an expression for the induced emf across the rod when it moves with speed v.
(iii) Using the results of (i) and (ii) together with Newton’s laws, derive an expression for the terminal speed vt attained by the rod.
(iv) Calculate the numerical value of vt for the given data.