Video: Determining the Direction of the Magnetic Field at the Center of a Circular Loop

A circular loop of wire is carrying a constant current 𝐼 in a clockwise direction as viewed from above. The current creates a magnetic field. Based on the diagram, state the direction of the magnetic field at the center of the coil.

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Video Transcript

A circular loop of wire is carrying a constant current 𝐼 in a clockwise direction as viewed from above. The current creates a magnetic field. Based on the diagram, state the direction of the magnetic field at the center of the coil.

Okay, in this diagram, we see our circular loop of wire and also that it carries a current 𝐼 in a clockwise direction around this wire as we’re looking at it. We’re told that this current creates a magnetic field, and we want to solve for the direction of that field at the very center of the coil, at this point P. To figure this out, we can recall what’s known as the right-hand screw rule. This rule recognizes that if we have a right-handed screw — say, this one here — then if we were to turn that screw in the direction that would make it go into some surface — say, a bit of wood or metal — then if that turning direction can be made to match up with the direction of a current in a circular loop of wire, then the direction the screw would sink into or be driven into that surface gives the direction of the resulting magnetic field at the center of the circular loop.

So for a right-handed screw, the direction the screw turns can be made to match current direction. And in that case, the tip of the screw points in the direction of the resulting magnetic field, specifically the magnetic field at the center of a current-carrying circular loop. So then, over here on our diagram, if we took a right-handed screw and arranged it so that we would turn that screw in the direction of the current in this loop, then we can see that the tip of the screw, as well as the direction the screw would travel, would be into the screen. So then that’s our answer for the direction of the magnetic field created at point P.

We can symbolize that field direction this way or simply write that it points into the screen. And we knew this thanks to the right-hand screw rule.

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