The bar in the diagram has mass m = 0.2kg, length i- 0.2m, resistance R = 0.3Ohm

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

a) induced emf = B L v

and current, i = e/R = B L v / R

to the right.

b) AT terminal velocity,

Fnet = F -mg = 0

F = mg in upwards direction.

and F in terms of B, L and v

F = IL x B = B^2 L^2 v / R

c)

F = B^2 L^2 v / R = m g

1.5^2 x 0.2^2 x v = 0.3 x 0.2 x 9.8

v = 6.53 m/s

d) R = B^2 L^2 v / mg

R is directlt propotional to v.

if R is decreased then v will be less.

hence slower.

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