A conducting rod of mass slides without friction on a pair of horizontal conducting…

PHYSICS · Single correct · CBSE · Physics · Electromagnetic Induction · Electromagnetic Induction

Problem

A conducting rod of mass

m

slides without friction on a pair of horizontal conducting rails separated by a distance

\ell

. The rails are connected through a resistor of resistance

R

, and a uniform vertical magnetic field

B

fills the region between the rails. At time

t=0

the rod is given an initial speed

v_0

along the rails. Neglecting air resistance, which expression gives the speed

v(t)

of the rod at a later time

t

? (a)

v(t)=v_0-\dfrac{B^{2}\ell^{2}}{mR}\,t

(b)

v(t)=v_0\,\exp\!\left[-\dfrac{B^{2}\ell^{2}}{mR}\,t\right]

(c)

v(t)=\dfrac{v_0}{1+\dfrac{B^{2}\ell^{2}}{mR}\,t}

(d)

v(t)=v_0\,\exp\!\left[-\dfrac{B\ell}{mR}\,t\right]