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Question

A conducting rod of mass m and length l is given a velocity V0 along the rails as shown is the figure. Magnetic field B exists perpendicular to the plane, then [Consider rails to be very long]

A
Time taken by rod to come to rest is mRl2B2.
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B
Distance travelled by rod before stopping is mv0Rl2B2.
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C
Heat generated across R till rod stops is mv202.
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D
Distance travelled by rod before stopping is infinite.
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Solution

The correct options are
B Distance travelled by rod before stopping is mv0Rl2B2.
C Heat generated across R till rod stops is mv202.

i=εR=BvlR
F=ilB (Deceleration)
a=Fm=ilBm
a=l2B2vmRvv0dvv
= -t0l2B2mRdt
lnvv0=l2B2tmR
v=v0el2B2tmR ...(1)
For v=0,t=.
a=vdvdx/vdvdx =- l2B2/vmR
vv0dv=l2B2mRx0dx \
v=v0l2B2mRx
v=0x=mRv0B2l2
The initial KE of the rod is 12mv20. This will be the heat lost after the rod comes to rest.

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