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Problem 15

You suggest that eddy currents can stop the motio…

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Problem 14

You have the apparatus shown in Figure P18.14. A circular metal plate swings past the north pole of a permanent magnet. The metal consists of a series of rings of increasing radius. Indicate the direction
of the current in one ring (a) as the metal swings down from the left into the magnetic field and (b) as the metal swings up toward the right out of the magnetic field. Use Lenz’s law to justify your answers.

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Video Transcript

in this question, we are asked to predict the direction of the induced current on the metal plate as it passes through a magnet whose North Pole is facing towards the metal plate. And we recognize that because the North Pole is here, the magnetic field exerted by the magnet is going to be coming out of the page from our perspective. And I will do you know this magnetic field asked the external magnetic field, Because it comes from an external force. In order to solve this question, we have to understand Lenses law, which states that the direction of the induced current so I sit in is such that it's induced. Byfield and I will write it as a species up in opposes the change in the magnetic flux through the oil the coils area produced by other objects. So let's look at how this law applies to this question card. A asks you in the case where the metal plate is swinging downward and is passing through the external magnetic field produced by the magnet. What is happening to the induced current if any? Well, let's notice that in this case the metal plate is experiencing an increase in the magnetic field because it is now entering the external magnetic field. So there is all of a sudden an increase in the magnetic flux experienced by the metal plate. So, Perlin, so small we're supposed to have and induced current that will eventually count her the effect of increasing magnetic flux. So which direction must this induced current be so that it fits lenses law? Well, let's recognize that because we want to decrease magnetic flux. To counter this effect, we need to have an induced my neck magnetic field that is in the opposite direction. Asked the external magnetic field. So I will denote this as Thean induced magnetic field and its direction is into the page from our perspective so that it opposes the external magnetic field direction. So in a sense, it is trying to balance out the fact that the metal plate is experiencing an increase in magnetic flux by inducing a magnetic field that will be the opposite of this. So what type of current will produce a magnetic field that points into the page on this metal plate? Well, if you use your right hand rule, wrap your fingers around the coil in such direction that your fingers are pointing into the page on the inside of the coil, and then you wrap it around your hand. You notice that your induced current is actually clockwise in this case. So for part A, the direction is clockwise. Let's apply the same logic to part B well as the metal plate. ISS Leaving Theo External Field. What's happening is that it will experience a decrease in the magnetic flux because it is now leaving the external field. It's going to experience less and less Ah, fewer and fewer numbers of magnetic field lines penetrating through its surface. Right. So to counter this effect, it wants to induce a magnetic field that will help uh, ree help, uh, reduced the decrease. That's a little hard to wrap your head around. Basically, um, the induced magnetic field must be in the same direction. Asked the external field. So that is trying Teoh minimize the effect of this decrease in flux. So now that you have, you know the direction of the induced magnetic field, which is also out of the page, you're going to apply right hand rule again. Wrap your fingers around the coil such that your fingers are coming out of the page and your thumb is going along the coil to indicate the direction of the induced current. And in this case we noticed that the current is in the opposite direction and it is counterclockwise. They should make sense because in thes two cases one you have an increasing flux, and so you want to produce a magnetic field that will reduce that increase. And so your current your induced current is clockwise, whereas if you have an opposite case than your current direction, should also be the opposite.

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