In a new lab experiment, two parallel vertical metal rods are separated by L = 1

Question

In a new lab experiment, two parallel vertical metal rods are separated by L = 1.0 m . A R = 2.0-resistor is connected from the top of one rod to the top of the other. A m = 0.22-kg horizontal metal bar falls between the rods and makes contact at its ends with the rods. A B field of0.50×104 T points horizontally between the rods. The bar should eventually reach a terminal falling velocity (constant speed) when the magnetic force of the magnetic field on the induced current in the bar balances the downward force due to the gravitational pull of the Earth.

Part A

Develop in symbols an expression for the current through the bar as it falls.

Express your answer in terms of the variables R, B, L, and terminal falling velocity v.

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Part B

Determine in symbols an expression for the magnetic force exerted on the falling bar (and determine the direction of that force). Remember that an electric current passes through it, and the bar is falling in the magnetic field.

Express your answer in terms of the variables R, B, L, and terminal falling velocity v.

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Part C

Determine the final constant speed of the falling bar for the given values.

Express your answer to two significant figures and include the appropriate units.

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Part D

Is this process realistic?

Is this process realistic?

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Explanation / Answer

motional emf at the ends of the rod is e = B*L*v

then current i = e/R = B*L*v/R

Part B) magnetic force on falling Bar F = B*i*L*sin(90) = B*(B*L*v/R)*L = B^2*L^2*v/R

direction of the force is vertically upwrds

Part C) B^2*L^2*v/R = m*g

v = m*g*R/(B^2*L^2) = 0.22*9.81*2/(0.5*0.5*10^-8*1*1) = 17.26*10^8 m/s

Part D) Not realistic ,becuse the speed of the rod is 17.2656*10^8 which is greater than speed of light (3*10^8) ,which is never possible for a body

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