## Illustration 27.4: Magnetic Forces on Currents

This Illustration shows current flowing through a wire. A current consists of charges moving through a conducting wire (1 coulomb of charge per second = 1 ampere). This can occur in a conductor since charges in a conductor are free to move in response to forces. Restart.

In the animation there is initially no magnetic field in the region shown. The electrons (the charge carriers that are free to move in conductors) travel in one direction, but the direction of the current is in the opposite direction (it is the direction positive charges would flow). There is nothing strange about this; it is just a convention. A positive current in a particular direction means that it is as if positive charges are flowing in that direction (this is equivalent to negatively charged electrons flowing in the opposite direction). What is the direction of the current in this animation? As there are negative charges moving to the left, there is a positive current to the right.

Turn on the uniform magnetic field pointing into the screen. Notice that we represent the field by a series of circles with "x"s inside them. Since we represent vectors with arrows, the "x" is supposed to represent what it would look like if you saw an arrow moving away from you. You would see the back view of an arrow and the "x" made by the feathered-end of the arrow. Similarly, for a magnetic field pointing out of the page, we use a series of circles with dots inside them (the view of an arrow point coming right at you). From where the electrons are located, what direction is the force on the electrons? Switch the direction of the magnetic field (out of the page). Now what is the direction of the force on the electrons? Notice that the electrons are moving to the left. We can use F = q v x B to determine the force. For the uniform magnetic field pointing into the screen, q is negative, v is to the right, and B is out of the page. Since v and B are perpendicular, we have that F = |F| = |q|vB. The right-hand rule (point your fingers towards v, curl them towards B, the direction your thumb points is the direction of v x B) gives downward for the force direction, but we must factor in the fact that we have negative charge. Thus, the force on the electrons in this case is upward. When we go through the same process for magnetic field (out of the page), we get that the force on the electrons is downward.

Change the direction the electrons are moving. Turn on the magnetic field into the page. What direction is the force now? If you followed the arguments of the previous paragraph, this should be easy.

With the electrons moving in the original direction, try a magnetic field pointing to the right. What is the direction of the force? What do you expect for a magnetic field pointing left? Try it. What can you conclude about the force on a moving charge (and, therefore, the force on a wire) in a magnetic field?

The force on a moving charged particle is perpendicular to both the velocity and the magnetic field (and the velocity and magnetic field cannot point in the same direction) and is described by the vector product or cross product F = qv x B. Remember that the charge on the electron is negative, so the force points in the opposite direction from v x B.

Illustration authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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