A copper rod of mass m slides under gravity on two smooth parallel rails l distance apart and set an angle θ to the horizontal. At the bottom, the rails are joined by a resistance R in figure. There is a uniform magnetic field B perpendicular to the plane of the rails. The terminal velocity of rod is

Question

A copper rod of mass m slides under gravity on two smooth parallel rails l distance apart and set an angle θ to the horizontal. At the bottom, the rails are joined by a resistance R in figure. There is a uniform magnetic field B perpendicular to the plane of the rails. The terminal velocity of rod is, m g R tan θ B 2 l 2, m g R cot θ B 2 l 2, m g R sin θ B 2 l 2, m g R cos θ B 2 l 2

MARKS App · Accepted Answer

Terminal velocity of the rod is attained when magnetic force on the rod (Bil) balances the component of weight of the rod ( m g sin θ ) , as in figure. So, Bil = m g sin θ B e R l = m g sin θ B l e R = m g sin θ B l B / V T R = m g sin θ v T = m g sin θ R B 2 l 2

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