uploaded imageA metal wire of mass m slides without friction on two horizontal r

Question

uploaded imageA metal wire of mass m slides without friction on two horizontal rails spaced a distance d apart, as in the figure below. The track lies in a vertical uniform magnetic field . Generator G produces a constant current i in the wire and the rails (even as the wire moves). Find the velocity of the wire's motion as a function of time, assuming it to be stationary at t = 0. (Use any variable or symbol stated above along with the following as necessary: B for the magnitude of . All quantities are in SI units. Enter the sign of the expression, taking right to be positive.) v = ?

Explanation / Answer

assuming,

Mass of rod, m
Current in rails, I
Magnetic field, B
Distance betweent he rails, d
Acceleration, a

Here due to motion,
Fn = m*a

Also,
Magnatic force geneerated due to current, Fb = I*B*L*Sin90

So, From newton Second Law, SUM(F) = 0
Fn - Fb = 0

Fn = Fb
m*a = I*B*L*Sin90

a = (I*B*L)/m

Since a = v/t (v is velocity, t is time)

v = I*L*B*t / m (Direction: to the left)

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