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 i

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

TestHub · 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, $Bil = m g \sin θ$

$B (\frac{e}{R}) l = m g \sin θ$

$\frac{B l e}{R} = m g \sin θ$

$\frac{B l (B / V_{T})}{R} = m g \sin θ$

$v_{T} = \frac{m g \sin θ R}{B^{2} l^{2}}$

Physics - Magnetism Question with Solution | TestHub

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