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.