# Current of Sliding Rod

1. May 16, 2015

### Angie K.

1. The problem statement, all variables and given/known data

If the U-shaped conductor in the figure has resistivity ρ (in Ω.m), whereas that of the moving rod is negligible, find the current I at time t. Assume the rod has length L, starts at the bottom of the U at t = 0, and moves with uniform speed v in the constant magnetic field B shown in the figure. The cross-sectional area of the rod and all parts of the U is A (in m2). Express your answer in terms of the given quantities.

2. Relevant equations

I = magnetic flux / Resistance

Resistance = p*L/A where p is the resistivity

3. The attempt at a solution

I = B*A*v/p*(L/A)

The current is equal to the magnetic field times the Area times the velocity, divided by Resistance (which is the resistivity times the Length times the Area)

What am I missing here because that formula that I calculated is wrong?

2. May 16, 2015

instead of going for that formula, go for the basic definition if induced EMF. As the rod moves with a velocity v, what is the emf induced on it?

3. May 16, 2015

### Angie K.

Emf would be : B*A*v

So then where does the resistivity come in?

4. May 16, 2015

no. emf is not BAv. Its Blv where l is the length of the rod. think about it. try to derive it.

5. May 16, 2015

### Angie K.

I'm taking an algebra based physics course so I'm not too comfortable with deriving but looking at an example of the derived form:

so after deriving the Emf equation, Emf = B L v and I would them be B L^2 v / p L/A ?

6. May 16, 2015

### Angie K.

Here is the picture for the problem, sorry forgot to post it

7. May 16, 2015

### TSny

How did L become L2.

Also, note that the resistance is in the U-shaped conductor. So, when using R = pL/A you need to consider the length of the U-shaped portion of the circuit. So, the L here is not the same as the L for the length of the moving rod. The length of the U-shaped portion will depend on the time t.

8. May 16, 2015

### Angie K.

I'm confused with what you would do with the time t. If the length changes based on t then can I just multiply the length by t?

9. May 16, 2015

### TSny

In the figure below, let x be the distance the rod has traveled. Can you express the length of the U-shaped portion of the circuit in terms of x and L? Then you can express x in terms of t.

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