In the figure is a U-shaped conducting rail that is oriented vertically and imme

Question

In the figure is a U-shaped conducting rail that is oriented vertically and immersed in a horizontal magnetic field (that points into the paper). The rail has no electrical resistance and does not move. A slide bar with mass m, length L, and resistance R can slide vertically without friction while maintaining electrical contact with the rail. The slide wire is released from rest. It accelerates downward because of its own weight and eventually reaches a terminal velocity v_term. Explain why the bar reaches a terminal velocity instead of accelerating uniformly under the force of gravity. Find an expression for the terminal velocity using only the given parameters and known constants. Then calculate the value of v_term if L = 20 cm, m = 10 g, R = 0.10 ohm, and B = 0.50 T

Explanation / Answer

(a)
It reaches terminal Velocity because there will be a Magnetic Force acting on the bar due to changing flux .
The changing flux gives rise to force opposite in direction to Gravity that causes the bar to reach a terminal velocity.

(b)
Induced emf due to changing flux,
e = B*l*v
I = e/R

Magnetic Force = Force due to gravity
F = I*L*B = m*g
e/R * L * B = m*g
B*L*Vterm * L * B = m*g*R
Vterm = (m*g*R)/(B*L)^2

Substituting Values,
Vterm = (10/1000 * 9.8 * 0.1)/(0.2*0.5)^2
Vterm = 0.98 m/s

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