A metal rod of mass m and length slides on frictionless parallel...

A metal rod of mass m and length

\ell

slides on frictionless parallel metal rails of negligible resistance, A resistance R is connected between the rails at their ends as shown in the figure. A uniform magnetic field B is directed into the plane of paper perpendicular to the plane of rails throughout the space. The rod is given an initial velocity

v_0

(towards right). No other force acts on the rod. Then A metal rod of mass m and length slides on frictionless parallel metal rails of negligible resistance, A resistance R

A metal rod of mass m and length slides on frictionless parallel metal rails of negligible resistance, A resistance R

Options

A $v(t)=v_0 e^{\frac{-B t_t}{m R}}$
Bthe rod stops after traveling a distance $x=\frac{m v_0 R}{B^2 \ell^2}$
Cthe total energy dissipated in resistance is $\frac{1}{4} m v_0^2$ i.e. half of the initial kinetic energy
Dthe total charge that flows in the circuit is $q=\frac{m v_0}{B \ell}$

Correct answer

D. the total charge that flows in the circuit is $q=\frac{m v_0}{B \ell}$

Step-by-step solution

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