Calculating Potential Difference for Moving Wire in Earth's Magnetic Field

[justagirl]

Hi, I was wondering if you can help me with the following question. I am totally stuck. I'm not sure I even understand the question. Any help or hint would be greatly appreciated!

This is the problem:
Over a region where the vertical component of the Earth's magnetic field is held in an east-west direction and moved horizontally to the north with a speed of 10m/s. Calculate the potential difference between the ends of the wire, and determine which end is positive.

End Problem.

I copied the above question verbatim, and I'm still trying to figure out what it means as it is worded strangely. I assume they're saying that the Earth's magnetic field is directed east-west and the wire is moving north at 10 m/s, perpendicular to the field.

I think this has something to do with motional emf, and the equation V = Blv plays some role. However, B and l are not given so I don't know. And the right hand rule probably has something to do with figuring out which end is positive.

That's all I can deduce. What do you think? Thank you so much for your time.

 

[Chen]

Think about a single positive charge in the wire. Since the wire is moving, you can attribute its velocity to the charges in it. So this positive charge has a velocity, and it's inside a magnetic field. You should know that in this situation a magnetic force acts on the charge $F_m = q\vec v \times \vec B = qvB\sin \alpha$. But we don't care about the strength of the force here, we are more concerned with its direction. This page describes an easy method to find the direction of the force:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/MagneticField/RightHandRule.html

So if know the direction of the magnetic force, you know where the positive charge "goes" as the wire moves through the magnetic field. Similarly, the negative charges will go to the other end of the wire since the force on them is on the opposite direction.

I probably explained things you had already known, but I'm not sure on what level you are so I explained them anyway. The potential difference cannot be calculated without further data.

 

[Chi Meson]

It is my opinion that some words are missing from this question. I believe it is supposed to say:

Over a region where the vertical component of the Earth's magnetic field is ...{some specific amount in teslas} and a wire is... held in an east-west direction and moved horizontally to the north with a speed of 10m/s. Calculate the potential difference between the ends of the wire, and determine which end is positive.


As given, there is no solution to the problem since no value for the magnetic field is provided. You could use 5 x 10^-5 T, since that is the approximate value for most of the US.