# In which direction does the current flow in a wire moving north to south along the Earth?

I stumbled upon this question and I can’t seem to figure it out. I think you have to use the right hand rule, but it doesn’t get me the right answer. The question is something along the lines of:

In which direction does the current flow in a wire moving from the northern hemisphere down towards the southern hemisphere? The wire is oriented east to west.

So, the magnetic field in the northern hemisphere points downward, and the wire is moving south, so also down. I don’t see how I could apply the right hand rule to this, since my thumb and fingers would both point downward. Apparently the answer is east, and I could get that if the magnetic field moved down into the earth, and the wire moved south along the earth. Is this where my mistake it? I always thought that the magnetic field moved down from the north to south, not necessarily into the earth.

• Hmm, I see your point. Assuming the wire is oriented east-west then if it's moving from north to south it isn't crossing any field lines. Having said this, the field is only parallel to the Earth's surface at the equator. In the northern hemisphere the field lines point slightly upwards out of the Earth and in the southern hemisphere the field lines point slightly downwards into the Earth (or is it the other way round - I can never remember which way magnetic field lines point). May 4, 2014 at 19:14
• The wire is oriented east to west. We never really explained the direction of the field lines in class except for the fact that they go North to South, so from the Northern Hemisphere towards the Southern when you're on the earth. My teachers explanation implied that the magnetic field points into the Earth, since he said the answer was east. May 4, 2014 at 19:21

## 1 Answer

You might be able to figure this out by looking at the following picture (source: http://www.unc.edu/depts/oceanweb/turtles/geomag.gif):

As you can see, the field lines point into the earth.

• Ah yes I see. I even drew this image when solving the problem. It's just that I never really imagined it in 3D, I always thought of as pointing into the earth only at the very poles, and otherwise moving along the poles. I see my mistake now, thank you. May 4, 2014 at 20:17
• You're welcome. Related point: when you buy a "good" compass, it will be rated for use at a particular latitude - the "south" tip of the needle is weighted to counter the force of the magnetic field that is pulling the "north" tip down. That force changes with latitude - so you buy a compass for "30-45 latitude", for example. See a discussion at attackpoint.org/discussionthread.jsp/message_671085 May 4, 2014 at 20:40
• One more thing, John Rennie mention the orientation of the wire. Why does it matter? Isn't the same same if the wire is east to west or west to east. I guess what I'm saying is what is the orientation of the wire, since it doesn't determine the current flow. May 5, 2014 at 5:24
• @Owell yes there is no "directionality" to the wire; it's just that the electrons, moving South across the field lines, experience a Lorentz force. They are constrained to move in the E/W direction because they have to stay in the wire. And you have convinced yourself that a B vector into the earth's surface will result in a net force in the easterly direction. Imagine a stretchy loop of wire all the way around the earth - Lenz's law should give you the same answer (current tries to counter the change in flux as the area increases). May 5, 2014 at 5:34