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. a) Explain why the bar reaches a terminal velocity instead of accelerating uniformly under the force of gravity. b) 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)

gravitational force on bar, Fg=m*g

and

force due to magnetic field, Fm=(B^2*l^2*v/R)

at equilibrium,

Fg=Fm

m*g=B^2*l^2*v/R

==>

v=m*g*R/(B^2*l^2)

===> terminal velocity, vt=(m*g*R)/(B^2*l^2)

b)

here,

if the U-shaped conducting rail moving downward

then,

magnetic flux through closed area increases and

induced current flows through rail,

hence force on the rail is upward which is balances with weight initially,

but

weight of the rail acts downward and its is greater the the upward foce,

therefore, it accelerate downward

c)

now,

terminal velocity,

vt=(m*g*R)/(B^2*l^2)

Vt=(10*10^-3*9.8*0.1)/(0.5^2*0.2^2)

vt=0.98 m/sec

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