BITSAT2018PhysicsMagnetic Effects of CurrentActual
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
Options
- Am g R tan θ B 2 l 2
- Bm g R cot θ B 2 l 2
- Cm g R sin θ B 2 l 2
- Dm g R cos θ B 2 l 2
Correct answer
C. m g R sin θ B 2 l 2
Step-by-step solution
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