How Is Terminal Velocity Calculated for a Sliding Wire in a Magnetic Field?

[pcandrepair]

Homework Statement

A U-shaped conducting rail that is oriented vertically in a horizontal magnetic field. The rail has no electric resistance and does not move. A slide wire with mass m = 10 g, L = 0.45 m, and resistance R = 0.10 Ω can slide up and down without friction while maintaining electrical contact with the rail. A magnetic field of B = 1.5 T is perpendicular to the rail as shown. Determine the terminal velocity (in m/s) of the slide wire if it is released from rest and falls under the force of gravity.

Homework Equations

F(B field) = I*(L x B)
F=mg
Induced motional emf = -B*L*v
Magnetic flux = B*L*x (with x being the other length of the rectangle which is (in this case) always changing)

The Attempt at a Solution

I am stuck on how to start this one. I'm pretty sure I have to find either the induced emf or the induced current. Then I could find the force of the magnetic field pushing up (against gravity) on the wire. Maybe? Any help on how to start this would be greatly appreciated! Thanks!

 

[anathema]

To begin, we can use the equation F = ma to find the acceleration of the slide wire. The only forces acting on the wire are the force of gravity and the force due to the magnetic field, so we can write: mg - F(B field) = ma. We also know that F(B field) = I*(L x B), so we can substitute this into our equation: mg - I*(L x B) = ma. Since we are looking for the terminal velocity, we can assume that the acceleration is zero, so the equation becomes: mg = I*(L x B). We can rearrange this to solve for the induced current: I = mg/(L x B).

Now, we can use the equation for induced motional emf to find the velocity of the slide wire. We know that the induced motional emf is equal to -B*L*v, so we can write: -B*L*v = mg/(L x B). We can rearrange this to solve for the velocity: v = -mg/(B^2*L). This gives us the velocity at any point in the slide wire's fall, but since we are looking for the terminal velocity, we can assume that the velocity is constant at this point. Therefore, the terminal velocity of the slide wire is v = -mg/(B^2*L).

I hope this helps you get started on solving the problem. Let me know if you have any further questions. Good luck!

 

[Moetasim]

I would start by identifying the known values and variables in this scenario. We have a U-shaped conducting rail with no resistance, a slide wire with specific mass, length, and resistance, and a magnetic field with a given strength and orientation. We also know that the slide wire is released from rest and falls under the force of gravity. From this, we can use the equations for force and induced emf to determine the terminal velocity of the slide wire.

First, we can calculate the force of gravity acting on the slide wire using the formula F=mg, where m is the mass of the slide wire and g is the acceleration due to gravity. In this case, the force of gravity would be 0.01 N.

Next, we can use the formula F(B field) = I*(L x B) to calculate the force of the magnetic field acting on the slide wire. Since the slide wire is moving in a vertical direction, we can assume that the force of the magnetic field is equal to the force of gravity. Therefore, we can set F(B field) = F=mg and solve for the induced current, I.

Once we have the induced current, we can use the formula Induced motional emf = -B*L*v to solve for the velocity of the slide wire. We know the values for B, L, and can now calculate the induced emf based on the induced current we found in the previous step.

Finally, we can set the induced emf equal to the resistance of the slide wire (Induced motional emf = R*I) and solve for the velocity, which would give us the terminal velocity of the slide wire as it falls under the force of gravity.

In summary, as a scientist, I would approach this problem by identifying the known values and variables, using relevant equations to calculate the forces and induced emf, and then solving for the terminal velocity of the slide wire.