In a new lab experiment, two parallel vertical metal rods are separated by one m

Question

In a new lab experiment, two parallel vertical metal rods are separated by one meter. A 2.0 ohm resistor is connected from the top of one rod and the top of the other. A 0.20 kg metal bar falls between the rods and makes contact at its ends with the rods. A magnetic field of strength 0.50 x 10-5 T points horizontally between the rods. The bar should eventually reach a terminal velocity when the magnetic force on the induced current in the bar balances the force of gravity on the bar. Your instructor asks you to develop, in symbols, expressions for the current flowing thorough the bar as it falls and the magnetic force exerted on the bar. Also determine the direction of the force. What is the final constant speed of the bar? Is this a realistic process? (Please show all the process and all the graphes needed)

Explanation / Answer

Induced EMF = BLv

and EMF = iR

iR = BLv

i = BLv / R

...................................................

force due to magnetic field = iLB   = B^2 L^2 v / R    .....upwards

gravitational force = mg

so at terminal speed ;

mg = B^2 L^2 v / R

v = Rmg / B^2 L^2    = 2 x 0.20 x 9.81 / ( (0.50 x 10-5)^2 x 1^2 )

v = 1.57 x 10^11 m/s

this is more than speed of light . This is not realistic.

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