Finally, we solve for direction using the right-hand rule. We point our hand in the direction that the
particle is traveling—to the right. Next, we curl our fingers upward, so that they point in the same
direction as the magnetic field. Our thumb points out of the page. BUT WAIT!!! We’re dealing with an
electron, which has a negative charge. So the force acting on our particle, and therefore the particle’s
acceleration, points in the opposite direction. The particle is accelerating into the page.
Magnetic Force on a Wire
A current is simply the flow of positive charges. So, if we put a current-carrying wire perpendicular to a
magnetic field, we have placed moving charges perpendicular to the field, and these charges experience a
force. The wire can be pulled by the magnetic field!
The formula for the force on a long, straight, current-carrying wire in the presence of a magnetic field
is
This equation says that the force on a wire equals the current in the wire, I , multiplied by the length of the
wire, L , multiplied by the magnitude of the magnetic field, B , in which the wire is located.
Sometimes you’ll see this equation written as F = ILB (sin θ ). Just like the equation for the force on a
charge, the θ refers to the angle between the wire and the magnetic field. You normally don’t have to
worry about this θ because, in most problems, the wire is perpendicular to the magnetic field, and sin 90°
= 1, so the term cancels out.
The direction of the force on a current-carrying wire is given by the same right-hand rule as for the
force on a charged particle because current is simply the flow of positive charge.
What would happen if you had two long, straight, current-carrying wires side by side? This is a
question that the writers of the AP exam love to ask, so it is a great idea to learn how to answer it.
The trick that makes answering this question very easy is that you have to draw the direction of the
magnetic field that one of the wires creates; then consider the force on the other wire. So, for example ...
Two wires are placed parallel to each other. The direction of current in each wire is indicated above.
How will these wires interact?(A) They will attract each other.
(B) They will repel each other.
(C) They will not affect each other.
(D) This question cannot be answered without knowing the length of each wire.
(E) This question cannot be answered without knowing the current in each wire.Let’s follow our advice and draw the magnetic field created by the left-hand wire.