1. The scene — bend the wire into a ring
You already met one big idea before this: a wire carrying current makes a magnetic field around it. The field does not just sit on the wire. It fills the space around the wire.
Now picture a straight wire carrying current. Wrap your imagination around it. The magnetic field lines around it are circles — circles that wrap around the wire like bangles on an arm.
A magnetic field line is just a path that shows which way a tiny compass needle would point at that spot. Where the lines are crowded close together, the field is strong. Where they spread out, the field is weak.
So far the wire is straight. Now do one thing in your head. Take that straight wire and bend it into a single round loop, like bending a piece of copper wire into a ring or a bangle. Current still flows through it, all the way around.
Here is the question this whole topic answers: what does the magnetic field look like now, especially right in the middle of the ring?
Stop scrolling. Try it in your head before reading on.
You can now picture the setup: a flat circular loop of wire, current running around it, and we want to know about the field at its centre.