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A uniform wire of mass m and length l slides freely along parallel rails on application of force F which starts acting at t = 0. Resistance of circuit is zero. System is placed in uniform magnetic field B, perpendicular to plane of figure. What is current through capacitor at any time t. (Ignore any inductance)

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a

BICFm+B2I2C

b

BICFmt

c

BICFt2m

d

BICFt2m+B2I2C

answer is A.

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Detailed Solution

qC=vBl ⇒⇒⇒ (1) net force= F-ilB=ma⇒⇒(2) from (1) dqdt1C=dvdtlB i1C=aBl a=iCBl substituting in (2) F-ilB=miCBl F=imCBl+lB i=FmCBl+lB=FCBlm+CB2l2

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A uniform wire of mass m and length l slides freely along parallel rails on application of force F which starts acting at t = 0. Resistance of circuit is zero. System is placed in uniform magnetic field B, perpendicular to plane of figure. What is current through capacitor at any time t. (Ignore any inductance)