How Does a Falling Metal Bar Generate Electricity in a Magnetic Field?

[Mightyducks85]

1. A 50 g horizontal metal bar, 12 cm long, is free to slide up and down between two tall, vertical metal rods. A 0.060 T magnetic field is directed perpendicular to the plane of the rods. The bar is raised to near the top of the rods, and a 1.0 Ohm resistor is connected across the two rods at the top. Then the bar is dropped. What is the terminal speed at which the bar falls? Ignore air resistance.

2. I= ε/R= (vlB)/R

I is current, ε is motional emf, R is resistance, v is velocity, l is length, B is magnetic field.



3. I don't even know where to start. I know that R= 1.0, l= .12 m, B= 0.060 T. What do I do with the 50 g?

 

[kuruman]

I will start you off by asking and answering the first question. You have to answer the rest to get going.

Q0. What does "terminal velocity" mean?
Ans. That the velocity reaches a final value that stays the same.

Q1. If the velocity stays the same what is the value of the acceleration?
Q2. If the acceleration has that value what does that say about the net force on the bar?
Q3. How many forces act on the bar when it reaches terminal velocity?
Q4. Given all your previous answers, what is the relation linking the forces acting on the bar?

 

[tomcue]

I would first analyze the given information and identify the relevant equations that can help solve the problem. In this case, we are dealing with a magnetic field, a moving conductor, and a resistor, so the equation for motional emf (ε = Blv) and Ohm's law (I = V/R) would be useful.

To solve for the terminal speed, we need to find the velocity (v) of the bar when the current (I) passing through the resistor is at its maximum. To do this, we can equate the motional emf equation to Ohm's law, since the current will be at its maximum when the motional emf is equal to the voltage across the resistor.

ε = Blv = V = IR

Substituting the given values, we get:

(0.060 T)(0.12 m)v = (1.0 Ω)(I)

We can now solve for the current (I) by using the fact that the mass of the bar (50 g) will be equal to the force of gravity (mg) acting on it when it reaches terminal velocity.

I = mg = (0.05 kg)(9.8 m/s^2) = 0.49 N

Substituting this value into the equation above, we get:

(0.060 T)(0.12 m)v = (1.0 Ω)(0.49 N)

Solving for v, we get:

v = (0.49 N)/(0.060 T)(0.12 m)

v ≈ 6.8 m/s

Therefore, the terminal speed at which the bar falls is approximately 6.8 m/s. This is the maximum speed that the bar will reach as it falls between the two vertical rods, under the influence of the magnetic field and the resistor.