Using the Right-Hand Rule

Right-hand rule

Ever wonder how physicists identify one another? The right-hand rule is the closest thing that physics has to a gang sign. Make a gun shape with the thumb and first two fingers of your right hand, and then point the middle finger to the left—or straight down, depending on how you hold your gun.
Image showing a hand in the right-hand-rule configuration
Now you’re in the gang. As long as you use your right hand. Using your left hand will get you kicked out faster than you can say “may the mass-times-acceleration be with you”. In this article, we’ll talk about the way that this sign is used to help physicists’ remember the direction of magnetic forces.

Where does it come from?

The right-hand rule is based on the underlying physics that relates magnetic fields and the forces that they exert on moving charges—it just represents an easy way for physicists to remember the directions that things are supposed to point. Occasionally a physicist will accidentally use his left hand, causing him to predict that the magnetic force will point in a direction opposite the true direction!

Moving charges

When charges are sitting still, they are unaffected by magnetic fields, but as soon as they start to move, the magnetic field pushes on them. But, the direction in which the field pushes on charges is not the same as the direction of the magnetic field lines. It instead looks more like this:
Image showing lorentz forces
We can remember this diagram using the right-hand rule. If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge. When you’re dealing with negative charges—like moving electrons—the force points in the opposite direction as your thumb.
Diagram of moving charge, magnetic force, and magnetic field line on a hand making the right-hand rule gesture

Current in a wire

When we talk about conventional current in a wire, we’re talking about the way positive charges move through a wire. Since we know that current is just moving charges, the wire will also be affected by a magnetic field in the same way as a single moving charge, but only when there is a current passing through it.
The right-hand rule applied to a conductive wire
We can use the same right-hand rule as we did for the moving charges—pointer finger in the direction the current is flowing, middle finger in the direction of the magnetic field, and thumb in the direction the wire is pushed.
The right-hand rule can also be used to remember the direction of the axes in a standard x, comma, y, comma, z coordinate system: the thumb points in the positive x direction, the first finger in the positive y direction, and the middle finger in the positive z direction.

Magnetic field caused by current in a wire

Not only are moving charges affected by magnetic fields, they can also create them. We can find the magnetic field that is caused by moving charges using a second right-hand rule. The magnetic field made by a current in a straight wire curls around the wire in a ring. You can find it by pointing your right thumb in the direction of the current in the wire and curling your fingers. Your fingers will be curled in the same direction as the magnetic field around the wire.
A magnetic field around a wire with current moving upward
It turns out that you can do the opposite of this rule to figure out the direction of the current in a wire if you already know the direction of the magnetic field. Point your thumb in the direction of the magnetic field this time and curl your fingers just as before. This time, the circular direction of your fingers tells you the direction of the current that creates the magnetic field.
The right-hand rule applied to a coiled wire
This last case represents what happens in an electromagnet in which current is run through a wire wrapped in the shape of a coil. This coil generates magnetic field lines that point in the direction of the coil’s long axis.
One way to remember these two coiling right-hand rules is that straight magnetic field lines are caused by circles of current, and straight lines of current cause circular magnetic fields. The right-hand rule allows us to remember both cases with a single hand gesture.

Consider the following: the magnetic field in an MRI

In MRI, or Magnetic Resonance Imaging, the patient lies in a strong stationary magnetic field that is used to align the individual protons attached to water molecules throughout her body. This alignment process is the first step in a measurement that uses small deviations of the protons from their alignment with the field in order to map out the density and structure of various parts of the patient’s body.
Basic MRI requires a strong magnetic field to be created in just one direction: along the axis of the body. For this reason, one configuration of the device consists of a giant electromagnet coil that surrounds the patient’s body. As we’ve learned from the right-hand rule, the current that travels in a spiral around the patient generates a magnetic field that points in a straight line along the patient’s body.
The magnetic field line and current direction in an MRI

Attribution

This article is licensed under a CC-BY-NC-SA 4.0 license. https://creativecommons.org/licenses/by-nc-sa/4.0/