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=−l2B2vmR⇒∫vv0dvv = -∫t0l2B2mRdt lnvv0=−l2B2tmR ⇒v=v0e−l2B2tmR ...(1) For v=0,t=∞. a=vdvdx⇒/vdvdx =- l2B2/vmR ∫vv0dv=−l2B2mR∫x0dx \ ⇒v=v0−l2B2mRx v=0⇒x=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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