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A conducting bar of mass m and length l ...

A conducting bar of mass m and length `l` moves on two frictionless parallel rails in the presence of a constant uniform magnetic field of magnitude B directed into the page as shown in the figure . The bar is given an initial velocity `v_(0)` towards the right at t = 0. Then the

A

Induced current in the circuit is in the clockwise direction

B

Velocity of the bar decreases linearly with time

C

Distance the bar travels before it comes to a complete stop is proportional to R

D

Power generated across the resistance is proportional to l

Text Solution

Verified by Experts

The correct Answer is:
C
`F=iBl" "rArrveca=(iBl)/m" "...(i)`
`varphi=BA" "rArr(dvarphi)/dt=Bl(dchi)/dt`
e = Blv
`i=e/R=(Blv)/R" "...(ii)`
By eq. (i) and (ii)
`a=((Blv)/R)(Bl)/m=(B^(2)l^(2)v)/(Rm)`
`a=v*(dv)/(dchi)=(B^(2)l^(2)v)/(Rm)`
`dv=(B^(2)l^(2))/(Rm)intdchirArrv=(B^(2)l^(2)chi)/(Rm)rArrchi=(Rmv)/(B^(2)l^(2))rArrchipropR`.
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