A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in Fig 6.11. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field .


(i) Write down equation for the acceleration of the wire XY.


(ii) If B is independent of time, obtain v(t), assuming v (0) = u0.


(iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.



Given: - mass of the wire m

magnetic field applied in


(i). At time t let XY be at x =x(t), magnetic flux association with area ACYX



induced EMF e =


(apply product rule)



induced current


Force on XY is F = Bil




acceleration of the wire is


(ii) when B is independent of time t is constant w.r.t time t



hence



but




integration on both side






when t= 0,



(iii)


=


power lost =


=


=


= decreases in kinetic energy


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