Two longparallel horizonal rails , a distanced apartand eachhavinga resistance lambdaper unit lengthare jointed at oneendby a resitance R. A perfectlyconducting rodMN of massm is free to slide along the rails . AvariableforceF is appliedto the rodMN , such that ,as therd moves, a constantcurrent i flowsthrough R. (a) Find the velocity v and the forceF as functionof thefunction ofthe distance x of the rod from R. (b) Whatfractioneta of the work done by Fpersecondinconverted into heat ?

Two longparallel horizonal rails , a distanced apartand eachhavinga re

1.	Two longparallel horizonal rails , a distanced apartand eachhavinga resistance lambdaper unit lengthare jointed at oneendby a resitance R. A perfectlyconducting rodMN of massm is free to slide along the rails . AvariableforceF is appliedto the rodMN , such that ,as therd moves, a constantcurrent i flowsthrough R. (a) Find the velocity v and the forceF as functionof thefunction ofthe distance x of the rod from R. (b) Whatfractioneta of the work done by Fpersecondinconverted into heat ?
Answer» ANSWER :`V=((R+ 2xlambda)i)/(Bd) F=B+(2mlambdar^(2)(R + 2 x lambda))/(B^(2)d^(2)),eta =(R)/((R+2 x lambda)+(2 lambdax (R+2x lambda )^(2))/(B^(3)d^(3)

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