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