A bar of mass m, length d. and resistance R slides without friction in a horizon

Question

A bar of mass m, length d. and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in the figure below. A battery that maintains a constant emf epsilon is connected between the rails. A constant magnetic it perpendicular, in the outward direction, to the plane of the page. Assuming the bar starts from rest, derive an expression for the speed of the moving bar which varies as a function of time t. [Use the following hints (not necessarily in this order): 1) Use the loop rule. 2) Use the magnetic force in combination with newton's law. 3) To substitution and separation of variables. 4) You need to include another emf.]

Explanation / Answer

Current=e/R

Force=ilB=edB/R

acceleration=F/m=edB/Rm

v=u+at=edBt/Rm

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