Three Right Hand Rules of Electromagnetism

Teaching electricity and magnetism is complicated by the challenge that the magnetic forces are perpendicular to the motion of the particles and currents. This requires a three-dimensional perspective which can introduce a variable of a "wrong" direction. To prevent errors, let us be "right" and use the right-hand rule.

Some would claim that there is only one right-hand rule, but I have found the convention of three separate rules for the most common situations to be very convenient. These are for (1) long, straight wires, (2) free moving charges in magnetic fields, and (3) the solenoid rule – which are loops of current. Calling these "rules" is the right name. They are not laws of nature, but conventions of humankind. We use rules to help us solve problems, laws would be the underlying cause as to why the rules work.

Danish Physicist and Chemist Hans Christian Ørsted

Electricity and Magnetism are connected phenomena, but at right angles to each other.  So we use the convention of the right hand to predict the direction of the fields relative to each other.

Rule #1 – Oersted's Law

Our story begins with Oersted's Demonstration, which was performed for the first time during a lecture in 1821. What Oersted showed for the first time that when a current carrying wire passes over a compass the needle – which is a magnet – the needle deflects. When it is underneath the magnet it deflects the other way. The direction that the magnet points is parallel to the magnetic field around the wire. And you can predict that with your right hand!

Point your right hand's thumb along the flow of current – defined as the flow of positive charge. Now curl your fingers as if they were wrapping around the wire. The direction that your fingers point, is the field. I sometimes like to call this the RIGHT-HAND CURL, or Ampere's Law. Ampere himself described it as the face of a clock: if the current flows into the face of the clock then the magnetic field would wrap clockwise.

A good way to demonstrate this phenomenon is with a set of the Small Clear Compasses. When these are wrapped around a vertical wire, with no current, they will all initially point North. But, if the current is switched on, the compasses will align in a loop around the current. It is important to note that the compasses do affect each other, so finding the right distance between them can help make the demonstration more dramatic.

Rule #2 – The Lorentz Force

This second right-hand rule is usually applied to freely moving charges, called cathode rays, or otherwise to push on electric currents.

A cathode ray tube computer screen is one vivid way to demonstrate the Lorentz Force. The screen is illuminated by moving electrons and moving charges are pushed about by magnetic fields.  This is a surprise to many people who think that magnets only affect metals such as iron and nickel.  (After using the CRT just leave it unplugged for a few minutes and that will restore almost all of the original screen color.)

Since electric current is made of moving charges we can also push it around with magnets. One way to show this is with an Electric Swing Apparatus. This will highlight that the current, field, and force are all three at right angles.

Using your right hand, the current flows from positive to negative – thumb.  The magnetic field – pointer finger – is directed from North to South (that usually means from red to blue).  The force on the current is perpendicular to both of these and is predicted by your middle finger.

This 2nd rule is usually called the Lorentz Force named after H. A. Lorentz, a contemporary of Einstein, although its effects were known at the time of Michael Faraday.

Now, some people and some books prefer to use the palm to represent the force, that would be current field force (open hand).

Another way to demonstrate this is with the Electricity and Magnetism Light bulb demo. When there is alternating current, the wire vibrates, but when it is direct current we can apply force in a specific direction. Using your right hand, it is possible to predict the direction the current is flowing.

For the flow of currents, which are the imagined flow of positive charge, it is appropriate to use your right hand.  But when it comes to negative currents, such as electrons, it is appropriate to use your left hand, which generates the opposite result that a positive charge would experience.  If one wishes to demonstrate the Lorentz force on a CRT, it helps to know to emphasize "use the left-hand rule for negative charges."

Rule #3 – The Solenoid Rule

An air core solenoid can act just like a bar magnet. Repelling north and attracting south. In fact – if you trace the magnetic field with a compass, you can see that it truly matches the behavior a bar magnet perfectly

Using a third right-hand rule, we can we predict which side of the coil is north.

Let your curling fingers be the direction the current is flowing. It is looping around. Then your thumb will be NORTH end of the electromagnet.

Left Hand Rule

The right-hand rules assume conventional current, that is… current flows from positive to negative. College-based courses all go with that concept. NOT ALL high school physics courses use that concept. For example, some high schools use the “left-hand” rules because it deals with ELECTRON FLOW, that is… current flow from negative to positive (the direction that electrons flow from a battery for example).

The hand rules work the same but they are based on two different current concepts. In this blog we focused strickly on the right hand rule.

Replicating Oersted’s demo is quite easy to do. I am using about 5 amps.

As the current flows upward, the magnetic field will wrap around.

Normally they just point North, but when I turn the current on we see them all pointing around it, just as we predict with our right hand.

This cathode ray tube computer screen was originally all red. But these magnets have deflected the electrons from landing on their proper pixels.

The magnetic field acts on the current in 3D.

Fingers are directed along the vectors using the right hand.

The filaments of the Edison-style bulb are deflected.

The solenoid will behave exactly like a bar magnet with a clearly defined north and south pole.

The north end of the solenoid repels the north end of this bar magnet.

James Lincoln