Electromagnetism, finding potential difference

[physics604]

1. Four conductors of equal length are each moved through a uniform magnetic field moving away from us (into the page) in different directions and with different speeds, as shown in my attached diagram. While the four conductors are being moved through the field, in which conductor will the largest potential difference be induced?

A. Conductor A
B. Conductor B
C. Conductor C
D. Conductor D


In summary:

Conductor A is moving up, v=1.0 m/s
Conductor B is moving right, v=2.0 m/s
Conductor C is moving left, v=4.0 m/s
Conductor D is moving down, v=3.0 m/s

Homework Equations

ε=Blv

The Attempt at a Solution

Using ε=Blv, I know that the magnetic field (B) and the length of the conductors (l) all have to be constant. So I know that the only variable changing is the velocity (v).

Since Conductor C is moving the fastest (v=4.0 m/s) and has the largest value, it would result in the greatest ε.

However, the answer is Conductor D (v=3.0 m/s). I don't understand why.

 

[TSny]

Hello. Is it possible to attach the diagram so we can see how the conductors are oriented?

 

[physics604]

Sorry, I forgot about that.

 

[TSny]

In ε = Blv, l is the dimension of the conductor perpendicular to v.

 

[physics604]

So if the l is parallel to v, there would be no ε induced?

I thought that for this equation, it was only v that had to be perpendicular to B (magnetic field).

 

[TSny]

So if the l is parallel to v, there would be no ε induced?

That would be true if the conductor had no thickness perpendicular to v.

I thought that for this equation, it was only v that had to be perpendicular to B (magnetic field).

You need to know the correct interpretation of l in Blv. For example, look at the attachment and decide what you would use for l for figures (a) and (b).

 

[physics604]

a) I would use 1.0

b) I would use 2.0

This is because the positive/negative charges are on the top/bottom of the rectangles so the lengths are taken from the side.

 

[TSny]

a) I would use 1.0

b) I would use 2.0

This is because the positive/negative charges are on the top/bottom of the rectangles so the lengths are taken from the side.

Yes. Good.