Question

In a new lab experiment, two parallel vertical metal rods are separated by L = 1.4 m . A R = 2.0-Ω resistor is connected from the top of one rod to the top of the other. A m = 0.18-kg horizontal metal bar falls between the rods and makes contact at its ends with the rods. A B→field of 0.50×10−4 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.
1)

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.

Answer 1

Answer:

Explanation:

Let v be the terminal velocity of the bar .

emf induced in the bar of length L

= B L v where B is the value of magnetic field.

current  i in the circuit containing resistance R

i = induced emf / R

BLv / R

Magnetic force in upward direction in the bar

F = BiL

= BL x BLv / R

B²L²v / R

For attainment of uniform velocity

magnetic force = weight

B²L²v / R = mg

so current

i = BLv / R

Answer 2

Answer:

The expression is: $I=\frac{BLv}{R}$

Explanation:

Please look at the solution in the attached Word file

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