A magnetic transportation system is constructed by placing a metal bar of mass M

Question

A magnetic transportation system is constructed by placing a metal bar of mass M on two long, parallel conducting rails of effectively zero resistance. The portion of the bar between the rails has length L and electrical resistance R. A potential difference of delta Vis applied across the ends of the rails, and a uniform magnetic field B perpendicular to the plane of the rails and bar fills the space between the rails. Assume the bar slides along the rails with zero friction while maintaining good electrical contact. a) If the bar is at rest, what acceleration (magnitude and direction) will it experience? I)) If the bar is moving to the right with speed v, what acceleration (magnitude and direction) will it experience at that instant? If the bar is started from rest and allowed to accelerate: c) What is the largest speed that the bar can ever reach? d) [BONUS] Find an expression for v(t), the bar's speed as a function of time, in terms of L, M, R, deltaV, and B.

Explanation / Answer

part A

at rest let I current flow through the wire

I = delta V/R

now force on wire F = BIL

acceleration

a = BIL/M

a = BL deltaV / M direction is towards right

part B

if bar move with velocity v then emf induced e = BVL

this emf oppose the delta V and current become

I = (delta V - BVL)/R

now acceleration

a = BL(delta V - BVL)/R towards right

Part C

at highest spped v(t) net force is zero

so delta V = Bv(t)L

v(t) = delta V/BL

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