Calculating Current in a Moving Rod U-Shaped Conductor Circuit

[Angie K.]

Homework Statement

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.

Homework Equations

I = magnetic flux / Resistance

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

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?

 

[AdityaDev]

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?

 

[Angie K.]

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?

Emf would be : B*A*v

So then where does the resistivity come in?

 

[AdityaDev]

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

 

[Angie K.]

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

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 ?

 

[Angie K.]

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

 

[TSny]

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 ?

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.

 

[Angie K.]

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.

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?

 

[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.