# A rod in a magnetic field?

• Durato
In summary, the problem asked you to think about how a moving rod in a magnetic field can produce a voltage. You can derive the motional emf formula by considering a single rod, or by considering the whole loop.f

#### Durato

OK, so I forget the exact problem, since it was on a test, but here's basically what it stated.

## Homework Statement

There's a magnetic field pointing directly into the page. A vertical rod, perpendicular to the magnetic field, is placed in it and is moved with a velocity v to the right.

Then, they show you a bunch of rods moving in different direction (but in the same plane of the paper). They ask you 'which one will produce the greatest voltage between both ends of the rod.'

I don't have pictures, since it was a test question, but what is bothering me is how a moving rod in a magnetic field can produce a voltage in the first place. Faraday's law states that V = rate of change of flux, but how is flux changing in this case? The rod is always in the magnetic field so the magnetic flux is always constant.

When i did look this up in the book, they 'derived' it by imagining that the rod was attached to a u-shaped loop. As the rod moved to the right, the area of the enclosed region would increase, thus increasing flux. But I don't see how this applies to a separate rod of metal.

Thanks!

At first I thought this question was about the Yankees playing at Boston.

The way to think about flux causing an emf is to consider whether or not field lines are cutting through the wire. IF it is just a single wire, then as it moves across a field, lines are continuously cutting through the wire. If it is a loop moving through a field, then the entire loop must be considered: a line that "cuts-in" can be canceled by a line that "cuts-out" of the loop.

Since the wire by itself is part of a larger loop (the circuit), then you can see that if the entire apparatus was moved through the field, then there would be no net change in flux. But since the straight wire is the only part of the circuit that moves across a field, then the flux inside the entire loop is obviously increasing.

I'm a little confused. They derived the voltage induced in a rod by pretending the rod was in a circuit (u-shaped metal with rod connecting the sides). But how does this apply to a single rod?

Hi Durato,

You don't have to derive the motional emf formula by assuming a loop. You can also derive by just considering a single rod. As the rod moves to the right, the charges inside the rod are moving to the right, and so the magnetic force will push them to one end of the rod (so one end becomes positive and the other becomes negative).

However, the electric force will try to pull these charges back together. When the electric and magnetic forces are in equilibrium, you can derive the motional emf formula.