 The fact that magnetic forces act at right angles to both the magnetic field and the current often has some interesting effects so let's look at some effects of magnetic forces. The ampere is the SI unit for current. It's also one of the base units. In other words, it's one of the units for which they have a definition and they make all the measurements of all the other units based on that. And it's based on the amount of force between two infinitely long wires. And so let's calculate what the force between two wires is. So if they're current carrying wires, let's have one have one current and the other have a different current. So we'll have I1 and I2 as the currents. So if you have two wires, why does one exert a force on the other? I suppose they both have mass. There'll be some kind of gravitational force between them, but that will be unbelievably tiny so we can ignore that. And they're made up of lots of charges, but their net average charge is almost zero. So there's an enormous number of positive charges, typically metal ions that form a lattice that make the wire and there's an enormous number of negative charges, the electrons that are free to flow and that's what gives you the ability to have current, but there's usually an equal number of both or very close to and so there's almost no electric field produced by the wire and there's almost no electric force between the wires. But there is a magnetic force because those moving charges that make the current do produce a magnetic field and the moving charges in the other current respond to that magnetic field. So I use the right hand rule to figure out the direction of the magnetic field due to I1. And if I put my right hand thumb along the direction of I1 and I see my fingers curling around, I see that they're going into the screen as it comes to I2 so I see the back of the arrow there and they'll be coming out of the screen on the other side. And how strong is that magnetic field? Well, I remember the formula, the strength of that magnetic field for an infinite wire is just going to be... and it's going to depend on the distance between them. Quick reminder, whenever you realize that you need some physical quantity in your calculation or formula, it's a great idea to draw it on your diagram because your diagram is where you can really understand what the physical situation is and make sure that your symbols that you're writing and the rest of your formulas and so forth make some kind of physical sense. So now we know the direction and the strength of the magnetic field that's at I2 due to the wire I1 and so we can work out the force on that. So remember, again, we need the right hand rule to get our fingers pointing along the direction of that current of our right hand and we sweep round to the magnetic field and so my fingers are pointing up along the screen here and they have to sweep down into the screen and that means that my right thumb is pointing to the left and so the force is going to be to the left and the current and the magnetic field are at right angles and so I can use the simple version of the formula. Remember, the formula just has an I in it. I have to remember which I. I'm experiencing a force due to the magnetic field so that's I2 and then I've got the length. If I have to draw a length here then I should put one in my diagram so that's the force and we've got the explicit dependence of the magnetic field up here and that's what we get for the magnetic force on the second wire due to the first wire. Now just from Newton's third law we should know that the force on the first wire due to the second wire should be equal and opposite. Let's check that. So supposing we look at the magnetic field on the first wire to the second wire if I put my right hand thumb in the direction of the second wire my fingers curl around and so I get a magnetic field due to the second wire that's indeed coming out of the board and so it's coming up towards our faces and then if I look at the force I'm going to have the current fingers pointing up and then the magnetic field coming out of the board so I'm going to have my fingers coming out towards me and that leads my right hand thumb pointing indeed back towards the second wire and if I plug in the formula here I'm going to have an I1 there instead and I'm going to have an I2 there instead and so I'm still going to have this same product and so indeed I'm going to have exactly the same force between the two wires in exactly the opposite direction and that's what Newton's third law tells us had to happen. So we can see that if we have two currents going in the same direction then those currents will attract. If instead we reverse the direction of one of the currents we'll reverse the direction of the force on it and so they will in fact repel and the other one is repeled as well because the magnetic field to that second wire will also be flipped and so that force on the first wire will be flipped.