 We've just looked at a lot of examples finding the direction of the magnetic field at a point. However, direction is only one component of the magnetic field. Strength is the other component. So let's look at a few examples finding the strength of a magnetic field due to a current. Here we have a wire carrying a current of 5 amps. And we want to find the strength of the magnetic field 3 meters away from the wire. When questions ask for magnetic field, or indeed any vector, it is always a good idea to give direction as well as magnitude, even if it isn't asked for. This is because vectors have both direction and magnitude. Direction is what distinguishes vectors from scalars. Since we need to give a direction, drawing a diagram is important to help with clarity. We are told that the current runs from north to south. So let's label a north and draw a current from north to south. Let's say this point is 3 meters away from the current. Then we want to find the strength of the magnetic field at this point. The right hand rule tells us that at this point the magnetic field would point out of the screen. And now all that's left is to find the strength of the magnetic field. We usually use the letter B to represent the strength of the magnetic field. And so B equals mu naught times i divided by 2 pi r. Mu naught is just a constant which we would look up or find on the formula sheet. The current we are given and the distance we are also given. So substituting in the numbers we get this expression. The pi's cancel and there's a common factor of 2 as well. And we end up with 3 times 10 to the negative 7 teslas. Now it's very hard to get an intuition on the strength of the magnetic field. So checking for plausibility of number is hard. We could do a units check though. That would be relatively simple in this case. The constant mu naught has units tesla meters per amps. Current has units of amps. 2 and pi are both unitless. And then we're dividing it by distance, so meters. The amps cancel, so this simplifies into tesla meters per meter. And then the meters cancel, which gives us teslas. Magnetic field is measured in teslas, so the units check out. And don't forget direction.