The bar in the diagram has mass m = 0.2kg, length I = 0.2m, resistance R = 0.3Oh

Question

The bar in the diagram has mass m = 0.2kg, length I = 0.2m, resistance R = 0.3Ohm. It slides without friction, and experiences no air resistance. The magnetic field points into the page and is 1.5T in strength. The conducting rails have no resistance. If the bar is falling with velocity "v" what is the current induced in the bar, in terms of the variables v, B, l, and R? Indicate its direction on the diagram. What is the magnetic force on the bar as it falls at terminal velocity (direction and magnitude)? Find the terminal velocity that the bar reaches. Will the bar fall faster, or slower if its resistance is decreased? Why?

Explanation / Answer

Here ,

for the falling bar

a)

current induced in the bar = induced emf/R

current induced in the bar = B * v * L/R

the current induced in the bar is B * v * L/R

the direction of current in the rod is to the RIGHT

b)

at the terminal velocity

net force on the rod is zero

magnetic force = - gravtity force

magnetic force = 0.2 * 9.8 upwards

magnetic force = 1.96 N in the upwards direction.

c)

magnetic force on the bar = B * I * L

magnetic force on the bar = B * ( B * v * L/R) * L

magnetic force on the bar = B^2 * L^2 * v/R

1.96 = 1.5^2 * 0.2^2 * v/0.30

solving for v

v = 6.53 m/s

the terminal speed of the bar is 6.53 m/s

part d)
if the resistance is decreased

lower EMF is needed for same current

hence , the bar will move slower.

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