Video: Understanding the Magnetic Field Created by a Current-Carrying Wire

Which of the four diagrams correctly shows the field lines of the magnetic field created around a current-carrying wire? [A] Diagram a [B] Diagram b [C] Diagram c [D] Diagram d

03:44

Video Transcript

Which of the four diagrams correctly shows the field lines of the magnetic field created around a current-carrying wire?

Taking a look at these diagrams, we see that each one has a wire with current running through the wire, either into or out of the page or, in our case, the screen. Each diagram shows magnetic field lines with directions indicated on them around the wire. We want to figure out which of the four diagrams correctly shows those field lines giving the current direction. As we get started figuring that out, let’s clear a bit of space on screen and then recall a rule that helps us figure out magnetic field direction based on current direction.

Whenever we have a current-carrying wire, say a wire like this, then once we know the direction of current in the wire, say that in this case it moves left to right, we can use what’s called a right-hand rule to figure out the way the magnetic field around this wire points. The way this rule works is we take our right hand and put it up to the wire, so that our thumb points in the same direction that the current flows. Once we’ve done that, the next step is to curl our fingers around the wire in the way that they naturally bend. That direction, the direction our fingers curl, is the direction the magnetic field around this straight wire points.

If we drew some field lines for this wire, they would be concentric circles around the wire that point in this direction shown. We’re gonna apply the test of the right-hand rule to each one of these four diagrams, to see which of the four correctly relates current direction with magnetic field direction. Let’s start out with the diagram a. This one says the copper wire is carrying current into the page. We can signify that this way, with an x. If we then get to apply our right-hand rule, then our first step is to put our right hand up to the wire in such a way that our thumb, that’s this part here, can point in the same direction as the current, in this case into the screen.

Then our next step is to curl the fingers on our hand in the direction they naturally curl. We see though that this is in the clockwise direction, whereas the arrow heads on these magnetic field lines are counterclockwise. That tells us that for diagram a the magnetic field line direction doesn’t agree with the current direction.

Let’s move on then to diagram b. In this instance, we see that the current is now moving out of the page. We’ll represent that by a dot in the centre of this wire. Once again, we’ll take our right hand and put it up to the wire and point our thumb in the same direction that current flows through the wire. In this case, that’s out of the screen. Then like before, we’ll curl our fingers around the wire in the direction that curl indicates the true magnetic field direction around this wire. But notice, the direction of this arrow is counterclockwise. But the arrow heads on the drawn in magnetic field lines point clockwise. This means that for option b as well, we don’t find the magnetic field lines pointing in the correct direction.

On then to option c, in this case the wire carries current into the page. So we’ll indicate that, just like we did in diagram a, with an x. And just like in diagram a, when we apply the right-hand rule, we find our fingers curl in the clockwise direction. But in this case, for diagram c, that direction agrees with the indicated direction on the magnetic field lines.

Right now, it looks like diagram c has a correct relationship between the direction of the current in the wire and the direction of the magnetic fields around the wire. As a last step though, let’s take a look at diagram d. In this case, current is going into the page or into the screen. We’ll indicate that once more with an x. And just like before, the right-hand rule indicates the magnetic field lines in this case should move clockwise. We see though that one of these arrow heads does move that way. But two of them do not. So that tells us that option d isn’t our correct choice either. So it all comes back then to option c. This is the one correct representation, out of these four diagrams, of the direction of the magnetic field lines around a current-carrying wire.

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