- #1

johann1301h

- 71

- 1

## Homework Statement

A rod with mass of m runs on rails in a magnetic field. The rails are connected with a wire at x = 0

so that the rod and the rails together with this wire form a closed circuit. The distance between the rails is L, and the resistance in the rod is R.

We assume that the rails and wire are ideal conductors, so that the total resistance in the circuit is R. At time t = 0, the rod moves in positive x-direction at velocity v0.

[/B]

https://uio-ccse.github.io/fys1120/homework/fig-week09/stav_skinner.svg

a)

Calculate the emf in the circuit using Lorentz's force law, and indicate the contribution from the different parts of the circuit.

b)

Calculate the emf with Faraday's law. Does this match the emf you calculated in the previous assignment?

c)

Find the size and direction of the current in the circuit. (With the clock)

d)

Determine the movement of the rod for t > 0. Can you check if the answer is correct using energy conservation?

**2. The attempt at a solution**

I believe i have solved b) and c), and a) shouldn't be to difficult, my struggle is with task d). So any help here is much appritiated!

b)

emf = BLv0

c)

I = (1/R)BLv0

d)

I think the rod wil move and then stop following a differential equation? I think the force on the rod is given by F = ILB, but the problem is that I (current) depends on the velocity of the rod! Any ideas?