Video Transcript
The diagram below shows a cross section of a current-carrying wire. The magenta arrow shows the direction of the magnetic field at point 𝑃. Fill in the blank. The direction of the magnetic field at point 𝑄 is blank the direction of the field at point 𝑃. (A) At a right angle to, (B) opposite to, (C) the same as.
In our diagram, the current-carrying wire is here, and we know that it can carry current either into or out of the screen. Like all currents, this current creates a magnetic field around itself. The direction of that magnetic field at point 𝑃 is shown by this arrow. We can use this magenta arrow to determine the direction of the current in the wire, either into or out of the screen. And that will let us solve for the direction of the magnetic field at point 𝑄.
We can understand the connection between magnetic field direction and current direction through something called a right-hand rule. Given a wire carrying a current we’ll call 𝐼, we can figure out the direction of the magnetic field created by this current using this rule. What we do is we point the thumb on our right hand in the direction of the current and then curl the fingers on that hand closed. The direction of that curl is the direction of the magnetic field created around this current-carrying wire. In this example then, that direction would look like this.
We can apply this rule to the current-carrying wire in our diagram. We’ve seen that the current in this wire can either point into or out of the screen. If that current pointed into the screen, then according to our right-hand rule, we would point our right thumb in that direction. And this would mean that the fingers on that hand can only curl closed in a clockwise direction. This would mean that for a point directly to the right of our current-carrying wire, as point 𝑃 is, the magnetic field created by a current into the screen would point downward rather than upward.
We know that the real magnetic field at that point is upward. So, we can say that the current in our current-carrying wire does not point into the screen. The only remaining option then is that it points out of the screen towards us. Pointing the thumb on our right hand in that direction, our fingers are able to curl closed in a counterclockwise direction. From this, we see that a point directly to the right of our current-carrying wire would indeed have a magnetic field that points upward. This agrees with what we see at point 𝑃.
But now, what about the magnetic field direction at a point directly above our current-carrying wire? That’s where point 𝑄 is. According to our sketch, the magnetic field at that point would point to the left. That exact phrase isn’t one of our answer options. But note that answer option (A) says “at a right angle to,” that is, at a right angle to the magnetic field direction at point 𝑃. Indeed, we see that there is such a relation between the magnetic fields at these two points. We see then that answer option (A) is correct.
Filling in the blank in our sentence this way, the sentence now reads “The direction of the magnetic field at point 𝑄 is at a right angle to the direction of the field at point 𝑃.”
