 The hand rules for magnetic field interactions can get pretty complicated. I mean there's these three different rules you've got to learn, but there's also sort of only two and in a way there's kind of like four. So let's look at a couple of examples so you can see some real life explanations of how to use the hand rules. Here's my first left hand rule. I'm going to take my hand and fingers and I'm going to point my thumb out to the side and curl my fingers like this. In the first hand rule my thumb is the direction of the current. The current is just the flow of charged particles through the wire or it could even be just a particle moving through space in one particular direction. My fingers are going to curl in the direction of the magnetic field that's produced by that charge. Here I have a straight piece of wire with a current moving up through it so I can use my first left hand rule. I point my thumb up in the direction of the current and my fingers curl in the direction of the magnetic field. You'll notice I also have some compasses down on that piece of cardboard. The compasses initially point to north but when the current is turned on, a magnetic field is created. This field goes in a circular pattern clockwise around the wire just as predicted by your first left hand rule. Now my second hand rule is going to have the same shape as the first one but the fingers and thumb are going to switch jobs. Now my fingers curl in the direction of the current and my thumb goes in the direction of the magnetic field. Now the really important thing to remember here is that my thumb is going to be the magnetic field that's inside of the loop of wire, not on the outside. Also my thumb will always point towards north of the magnet to which that coil of wire will become. Here's a loop of wire. Let's pretend we had a battery hooked up to it with electrons flowing through the wire. My fingers would curl in the direction of the electron flow and my thumb would point in the direction of the internal magnetic field the coil is producing. Here's that same loop of wire. In a moment I'm going to turn on the current and the electrons are going to go up the back of the wire and down the front of the wire. When that happens we get a magnetic field produced. The magnetic field points to the left which is exactly what my thumb would do if I applied the second left hand rule. In the third hand rule we finally introduce force. There's a couple of different ways you can hold your hand but this is the way I like to do it the most. I point my thumb out like this and then I point my index finger so it's at a right angle to my thumb. Then my middle finger juts out like that so it makes a right angle with my pointer index finger and with my thumb. Everything is mutually perpendicular. All of my fingers are at right angles to one another. Now in the third hand rule my thumb is going to be the current or the direction the charged particle is moving. My pointer finger is going to be the direction of the magnetic field and my middle finger is going to be the direction of magnetic force that's acting on the particle. Now that magnetic force is due to the external magnetic field that the charged particle finds itself in. Here's a cathode ray. There's a beam of electrons that are moving to the left. If I put a magnetic field near them I can bend them. Magnetic fields coming towards the screen, the electron flows to the left and the magnetic force acts down by the third left hand rule. There's sort of a fourth hand rule because if you're dealing with a positive particle instead of a negative particle you do the exact same series of steps but you just use your right hand instead of your left hand. You're going to use your right hand whenever you're dealing with positive charged particles moving through external magnetic fields. I can use my right hand to describe what's happening as this possibly charged proton moves into a magnetic field directed into the screen. My current will be going to the right so I'm going to point my thumb of my right hand in that direction. The magnetic field is into the screen so I'm going to put my pointer finger into the screen and I get a magnetic force going upwards. Therefore, that positive particle will curve up in the magnetic field.