Induced voltage difference in a magnetic field

[waazwag]

Homework Statement

(a) If the magnetic field $B$ is constant with respect to time, what is an expression for the induced voltage between the two ends of the rods? Moreover, which end of the rod is at higher voltage (the part that's rotating, or the point that's fixed) and in which direction do the electrons flow? Assume $B$ points out of the page, and the rod is rotating counterclockwise.


(b) Now suppose a conducting ring is added. The end of the rotating rod is always in contact with it. How do the answers in the preceding part change?


(c) Repeat the first part but now assume the magnetic field is time-dependent. Say it takes the form $B(t) = B_0 \sin(\omega_0 t)$ where $\omega_0$ is much smaller than $\omega$ so that the field oscillates in and out of the page.

Relevant Equations

Lenz's Law, Faraday's Law

Hi everyone,

I'm currently working on the problem listed above.

I'm pretty new to electrodynamics, and I'm learning on my own through a book. I was wondering if someone can please help me through this problem. Here are my thoughts:I think I need to use Faraday's Law of Induction for part (a), which says the induced EMF is $-d\Phi_{B}/dt$. However, since the B-field is constant with respect to time (and $\Phi_{B} = \vec{B} \cdot \vec{A})$, would this just mean that the answer to the first part of part (a) is zero? I'm not entirely sure which part has a higher voltage due to my previous answer. I think that the last part of this problem involves Lenz's law, but I'm not too sure about how to approach this either.

 

[BvU]

Hello @waazwag, !

I'm currently working on the problem listed above.

Yes, of course. But is the problem statement complete ? E.g.: what rods ? Moving or stationary w.r.t. $\vec B$ ?

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