2. Two parallel conducting rails, joined at the bottom, are separated by width w

Question

2. Two parallel conducting rails, joined at the bottom, are separated by width w = 15.00 cm. The U-shaped system is inclined by 40° to the horizontal, as suggested in the drawing with an assumed constant resistance of 4.00 x 10-3 . There is a vertical, uniform magnetic field pointing upward with a strength of 600 mT. A conducting rod of mass 0.050 kg can slide frictionlessly down the rails (staying parallel with the horizontal). As the rod is released and slides down, it begins to accelerate. As the rod slides downward, a current is induced in the rod, generating a braking force. Determine the current (in the rod, including direction of current flow) in the rod when the rod achieves its terminal speed, and what is that terminal speed? w = 15 cm 40

Explanation / Answer

a) Let I is the current flowing through the rod when the rod moves with terminal speed.

In the is case Net force along the ramp = 0

m*g*sin(40) - FB*cos(40) = 0

m*g*sin(40) - B*I*w*cos(40) = 0

m*g*sin(40) = B*I*w*cos(40)

==> I = m*g*sin(40)/(B*w*cos(40))

= m*g*tan(40)/(B*w)

= 0.05*9.8*tan(40)/(600*10^-3*0.15)

= 4.57 A <<<<<<<--------------Answer

B) let v is the terminal speed of the rod.

I = induced emf/R

I = B*v*w/R

v = I*R/(B*w)

= 4.57*4*10^-3/(600*10^-3*0.15)

= 0.203 m/s

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