KVPY SX SB Exam 2016 Question Paper

Question : 26 of 120

Marks: +1, -0

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

Induced current in the circuit is in the clockwise direction
Velocity of the bar decreases linearly with time
Distance the bar travels before it comes to a complete stop is proportional to R
Power generated across the resistance is proportional to l

Validate

Solution:

F=iBl

a={iBl}/m

ϕ=B.A

{dϕ}/{dt}=Bl({dx}/{dt})

ε=(B.lv)

i=ε/R={B.lv}/R

a=({Blv}/R){Bl}/m={B^2l^2}/{Rm}.v

⇒a=v.{dv}/{dx}={B^2l^2}/{Rm}.v

⇒∫dv={B^2l^2}/{Rm}.∫dx

⇒v={B^2l^2}/{Rm}.'X'[X={vRM}/{B'l^2}]

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