The bar in the diagram has mass m = 0.2kg, length l = 0.2m, resistance R = 0.3W.

Question

The bar in the diagram has mass m = 0.2kg, length l = 0.2m, resistance R = 0.3W.     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.

a)If the bar is falling with velocity “v” what is the current induced in the bar, in terms of the variables v, B, , and R? Indicate its direction on the diagram. [5]

b)What is the magnetic force on the bar as it falls (direction and magnitude)? [5]

c)Find the terminal velocity that the bar reaches. [5]

d)Will the bar fall faster, or slower if its resistance is decreased? Why? [5]

Explanation / Answer

a)

induced EMF

E = BVl

induced current

i = BVl /R

b)

Fb = ilB

Fb = B^2 l^2 v/R ( upward direction)

c)

for terminal condition

Fb = mg

Vt = 6.53 m/sec

d)

from the above equation Vt is directly proportional to terminal velocity

therefor R increases V increases

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