The Hall Magnetism Effect: Explanation and Demonstration

An interesting electromagnetic effect that appears in many solids is the Hall Effect. Ordinarily, a conductive material (like a metal) will have the same voltage anywhere on it, so if you try to measure the voltage across any two points on the two you will read zero. However, throw in a stationary magnetic field and run current through the metal, and suddenly you can detect voltage differences (and pass side currents through) various points on the metal. How can this be if the metal is conductive? Isn't the whole point of conductors that you can short things with them?

Today I'll be explaining the Hall Effect and why it occurs. I've managed to create a crude demonstration using a fork and a magnet, which will be shown later in this post.

This electric ion spacecraft thruster uses the Hall Effect to generate very high efficiency thrust and enable the exploration of the solar system.
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Currents and Magnetism

To start, I once again want to show you one of the fundamental equations of magnetism: The Lorentz force:

F = q(v x B)

This extremely important equation describes magnetic forces. F represents the force vector acting on a particle, v is the velocity vector of the particle, B is the local external magnetic field vector, and q is the value of the charge on the particle (q is just a number, not a vector). "x" denotes the vector cross product. Without going into how the cross product works, the essential takeaway is that magnetic fields can move charged particles. Put a charged particle in a magnetic field and nothing happens. Give the charged particle a kick, making it move off in some direction, and the particle will curve in a circular trajectory due to the magnetic force. The magnetic force in this case acts perpendicular to both the particle's velocity and the magnetic field.

Lorentz Force effects on a charged particle with a magnetic field coming out of your screen
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This works anywhere there are moving charges. This force effects many types of ionizing radiation (alpha, beta, proton, positrons, etc), allows your microwave oven magnetron to operate, and can exert pushing forces on ... electrical currents in a wire. When you connect a battery to a wire, electrical current flows through it. But on average all this current is, is charged electrons moving in the same direction. And, as moving charges, they will be pushed by the Lorentz force when they move through a magnetic field.

The Hall Effect

Now we are ready to examine the Hall Effect itself.

To see the Hall Effect, imagine placing a piece of metal on a table. Underneath the metal, place a big permanent magnet with the pole facing up. This will create a lot of magnetic field lines passing through the metal. Now, take a battery and connect one end to one side of the metal block and the other terminal to the opposite side of the metal. Once you do this, an electric field produced by the battery pushes electric charges in the metal (usually taking the form of electrons) between the two battery terminals.

But, there's a magnetic field here, pointing mostly up relative to the metal. Now the Lorentz Force kicks in on the electrons moving across the metal, and the cross product dictates that the electrons will be pushed to the side (which side depends on the magnetic field direction and some material properties). This small net force causes there to be more electrons on one side of the metal than the other. This causes a charge buildup and imbalance across the sides of the metal. Note that I'm referring to the sides perpendicular to the current flow - the charge doesn't build up on the two sides that have the battery connected.

And, where there is a difference in charge, there is typically voltage. I've said before that the voltage (potential) is the same anywhere in a metal, which is true for metals in equilibrium - that is, metals where all the charge isn't "moving". Since there's a current flowing through the metal, and a Hall Effect induced current pushing charges to the side, the metal isn't in electromagnetic equilibrium and the same-potential idea doesn't hold.

Diagram of a typical Hall Effect voltage
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This means that if we take a voltmeter and connect it across the sides of the metal (across the flow of current), we can measure the charge buildup and will detect a voltage that is not zero. Remember that measuring the voltage across metals ordinarily returns zero. The Hall Effect, caused by the buildup of charges via the magnetic field and current, produces a voltage across the metal. This voltage acts pretty much just like a voltage from a battery or any other DC source: You can charge capacitors with it, or heat up things, or even light up lights (although getting the voltage high enough to do that might be very difficult). In simple terms, the Hall Effect basically uses a magnet to produce a tiny battery perpendicular to the flow of electric current across another battery.

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And that's the Hall Effect. It's a somewhat straightforward application of basic electromagnetic equations. The strength of the effect depends primarily on the amount of current flowing through the metal, the magnetic field strength, and how many electrons are available in the metal chunk.

Using the Hall Effect

Maybe you are wondering if we can produce electrical power from this and power things like our homes - after all I just described the Hall Effect as producing "tiny batteries". However, this unfortunately isn't possible to my knowledge. In order to get a voltage from the Hall Effect to begin with, you need a flowing electrical current, which requires an electrical power source. So any energy derived from the Hall Effect would have to be created using another electrical power generator like a battery or wall outlet, and you wouldn't actually get any net power out.

However, the Hall Effect is incredibly useful. On the physics side, it can be used to determine the sign (positive or negative) of the charges flowing through a wire. For things like circuits and resistors, it doesn't matter if you model the current as positive charges flowing in one direction or negative charges flowing in the other direction. The Hall Effect, however, distinguishes between these two, and allowed scientists to determine that negatively-charged electrons were responsible for carrying currents rather than the positive charges of conventional current.

You can also use the Hall Effect to make a device to measure how strong a magnetic field is. This might sound like something that would only be done in a lab, but I bet your cell phone has one of these sensors in it right now, allowing it to act as a compass to point you north and turn off your phone when you close its magnetic case. If you've ever wondered how tablets know to turn off when their cases are shut, this is how.

This tiny, cheap semiconductor Hall Effect sensor lets you measure the strength of the magnetic field around you.
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Plenty of other applications exist, such as measuring the speeds of motors and figuring out how far away nearby objects are. One interesting one is the spacecraft propulsion thruster I showed at the beginning of the post. Hall-effect thrusters are high-efficiency electric thrusters, capable of producing thrust by ejecting charged ions with the help of the Hall Effect. This lets a spacecraft get much further on much less heavy fuel, enabling for distant exploration without the giant expensive rocket.

Another Hall Effect ion thruster
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Demonstration of the Hall Effect

I was able to make a very quick setup and actually demonstrate the Hall Effect myself.

I took a metal (conductive) fork and put it on top of a ring magnet from a microwave magnetron. The magnetic is polarized about the axis through the center, so most of the field going through the fork is now in approximately the same direction and quite strong.

I then attached alligator clips to the ends of the fork and connected this to a small 1.5 volt AAA battery. Shorting the circuit with the battery will result in current flowing through the fork, determined by the fork's electrical resistance and the battery's internal resistance.

I attached the clips from my multimeter leads across the two sides of the fork as shown. Setting the multimeter to voltage-measurement mode shows a voltage difference of ZERO, since the probes are shorted by a conductor (the fork).

Here's the setup with the battery disconnected:

This image shows no battery connected, so no current flows through the metal fork. This means that the fork is in electrostatic equilibrium, and the electric potential is the same everywhere on the metal fork. So, trying to measure voltage across the sides of the fork returns a value of zero, as expected - this is what shorting a circuit does.

This changes when I hook up the battery. This causes electrons to flow through the fork. The magnetic field coming out of the fork forces some of these electrons to the side, producing a Hall voltage across the sides of the fork and allowing me to detect the Hall Effect by reading the voltage across the fork perpendicular to the current flow. And, indeed, connecting the battery immediately caused the multimeter to read a tiny, but nonzero, voltage across the fork.

This is conclusive proof that the Hall Effect is occurring in the fork, since if it were not, it would be impossible to read a voltage across a single conductor. It is also a visible detection of the magnetic field surrounding the fork.

The tiny 0.1 millivolts of potential across the conductive fork give away the Hall Effect. Note that since the meter is reading negative, the electrons pushed over by the magnetic field have accumulated on the side of the fork with the red lead attached.

This tiny voltage difference is stable as long as I keep the battery connected, and immediately disappears when the power source is removed. This clearly shows the hand of the Hall Effect and Lorentz Force in action.

With modifications, a similar setup could be used as a magnetic field meter/detector. This would require knowledge of the fork's Hall coefficient (calculated using a metal's electron density), the exact current flowing through the fork, and a precise measurement of the Hall voltage produced across the side of the fork. Such a setup would let you back-calculate the magnetic field, allowing you to "see" a previously invisible but obviously present field.

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And, well, that's the Hall Effect. I hope you found this effect interesting and learned something new!

Thanks for sticking around to the end. Let me know if you have any questions or comments, or if I got something wrong. I'll try to upvote all non-spam comments with my little bit of voting power.

Thanks for reading!

All images not credited are my own. You are welcome to use them with credit.

Additional Sources:
Hofmann, Philip: Introduction to Solid State Physics
HyperPhysics Hall Effect