For the magnetic field created around a current-carrying wire the blank the current the blank the magnetic field.
This question is trying to probe our understanding of how the magnetic field links to the current of a current-carrying wire. So let’s start by drawing a quick diagram. Let’s say that this is our wire and the current in this wire is traveling in this direction, upwards.
We can label this 𝐼. We can use our right-hand rule, in this case, the right hand being very poorly drawn to help us work out which direction the magnetic field is going to be traveling in. If the current in the wire points in the direction of our thumb, then the magnetic field is going to be going round in the direction of our fingers. And so here’s the magnetic field the wire produces.
This right-hand rule is quite a useful technique to use by the way in the case of a current-carrying wire. You can remember the thumb as being the current and the fingers as being the magnetic field. Now we can recall that the magnetic field generated by a current-carrying wire depends on two things: firstly, the distance from the wire; and secondly, the current in the wire.
Looking at the first one, we know that the magnetic field is inversely proportional to the distance from the wire. In other words, it’s strongest when we’re near the wire, and it gets weaker as we go further away from it. Secondly, we can think about the current. Well a current is basically just a flow of charge. And specifically, current measures the rate of flow of charge.
In other words, it measures how much charge is flowing past a certain point per unit time. So a larger current means there’s more charge flowing through the wire per unit time. Either that or the charge is flying much quicker. Now we know that the magnetic field produced by a moving charge depends on the speed of that charge. So if the charges are flowing through this wire quicker, or in other words the current in the wire is larger, than the magnetic field produced must also be stronger.
Therefore, the current in the wire and the magnetic field produced by the wire are directly proportional. So we can choose two words to fill in the blanks that would reflect this relationship correctly. Here’s an example of a pair of words: larger and stronger. Putting these into the blanks, we have: for the magnetic field created around a current-carrying, wire the larger the current, the stronger the magnetic field.