Question Video: Identifying the Position of the Wire in a Slip Ring Generator | Nagwa Question Video: Identifying the Position of the Wire in a Slip Ring Generator | Nagwa

Question Video: Identifying the Position of the Wire in a Slip Ring Generator Physics • Third Year of Secondary School

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Diagram (a) shows a generator consisting of a loop of wire that spins in the uniform magnetic field created between two permanent magnets. Diagram (b) shows a cross section of the generator, showing the direction of the magnetic field and the path of the two sides of the wire loop. Diagram (c) shows the potential difference induced in the wire by this motion against time. Which point on the graph in diagram (c) corresponds to the position of the wire shown in diagram (b)?

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Video Transcript

Diagram (a) shows a generator consisting of a loop of wire that spins in the uniform magnetic field created between two permanent magnets. Diagram (b) shows a cross section of the generator, showing the direction of the magnetic field and the path of the two sides of the wire loop. Diagram (c) shows the potential difference induced in the wire by this motion against time. Which point on the graph in diagram (c) corresponds to the position of the wire shown in diagram (b)?

In this question, we are asked to think about the potential difference across a coil of wire in a generator. Recall that a generator uses electromagnetic induction to produce electricity. In a generator, a coil of wire is placed in between a north and south magnetic pole. In order to generate a current, mechanical forces are applied to a coil of wire to make it rotate. When the coil rotates, a potential difference is induced across the coil. This process is called electromagnetic induction.

Electromagnetic induction occurs when the magnetic field passing through a loop of wire changes. So, how does this process occur in generators? Well, when the coil of wire rotates, the magnetic field that passes through it changes. To make this easier to think about, let’s clear some space on screen and look at our generator from a slightly different angle.

Here, we’re looking along the axis of rotation of the coil. Even though the coil is still a rectangular loop, it appears to be a straight line from this perspective. Let’s imagine that the coil is rotating in this direction. We can also add the magnetic field lines onto our diagram, like this. At first, the coil is oriented parallel to the magnetic field. We can see that no magnetic field lines are passing through the loop. Now imagine the loop some time later, when it is perpendicular to the magnetic field. We can see that, now, several magnetic field lines are passing through the loop.

So, as the coil rotates, the magnetic field passing through it changes. This causes a potential difference to be induced across the coil. The magnitude of this potential difference is proportional to the rate at which the magnetic field passing through the coil changes. In other words, it doesn’t really matter how many field lines are passing through the loop. What matters is how quickly the number of field lines is changing. Using this idea, we can work out the magnitude of the potential difference induced across the coil at different points in the coil’s rotation.

Let’s start by thinking about the coil in its current position, perpendicular to the magnetic field. To make it easier to keep track of the coil, we’ll draw an arrow, showing which way the coil is facing. This allows us to call this side of the coil the front and this side of the coil the back. Here, we can see that there are four magnetic field lines passing through the coil, from back to front. So, how can we work out how quickly the magnetic field through the coil is changing?

Well, let’s think about what the generator would look like at the instants just before and just after the moment that the coil is perpendicular to the field. To make it easier to see, we’ve exaggerated the angle of the coil in these diagrams. In reality, the coils would be very close to being vertical. We can see that, in all the diagrams, there are still four magnetic field lines passing through the coil, from back to front. So, the magnetic field that passes through the coil isn’t changing very much at all.

Since the potential difference depends on the rate of change of the magnetic field through the loop, or how quickly the magnetic field through the loop changes, this means that the potential difference across the loop is zero. We can make a note of this by plotting this value on a graph of potential difference against time. We’ll say that the coil is perpendicular to the field when the time 𝑡 equals zero. So, this point goes here.

To help us remember how we work this out, we will also draw the orientation of the loop, down here. Now, let’s imagine the coil one-quarter of a rotation later, so that the coil is parallel to the magnetic field. The arrow we drew before is now pointing downwards, telling us that this side is the front and this side is the back. Like before, we can also draw the coil just before and just after this moment, to help us work out how quickly the magnetic field passing through the coil is changing.

Just before the coil is parallel to the field, there is one field line passing through the coil, from back to front. At the moment when the coil is parallel to the field, there are no field lines passing through the coil at all. Just after this moment, there is again one field line passing through the coil, but this time in the opposite direction, from front to back.

So, between these moments, not only does the number of field lines passing through the coil change, but the direction in which they pass through the coil also changes. This represents a very significant change in the magnetic field passing through the coil. In fact, this is actually the instant in the coil’s rotation where the rate of change of the magnetic field through the coil is the greatest. And so the potential difference induced across the coil reaches its maximum value at this moment.

Again, we can make a note of this by plotting this point on our graph, like this, and drawing the orientation of the coil. After another quarter turn of the coil, the coil is once again perpendicular to the field. Using the same logic as before, we can deduce that the potential difference across the coil at this moment is zero. After another quarter-turn, the coil is now parallel to the field. Just like before, this means that the magnetic field passing through the coil is changing at the greatest rate and that the magnitude of the potential difference across the coil has its maximum value.

However, because the coil is pointing in the opposite direction, compared to the last time it was parallel to the field, the change in the magnetic field occurs in the opposite direction. This means that the potential difference induced across the coil now has the opposite sign. So, this value gets plotted here on our graph. Finally, another quarter turn later, the coil is again perpendicular to the field, and the potential difference across it is zero.

We’ve now worked out the potential difference across the coil at various points during one rotation. Let’s now join these points with a curved line, like this. We have now drawn a diagram that shows how the potential difference induced across the coil depends on its orientation in the magnetic field. Our graph looks very similar to the one given to us by the question in diagram (c). So we should have everything we need to work out the solution.

To answer this question, we need to work out which of the labeled points on the graph corresponds to the orientation of the coil that is shown here. Before we think about the graph, let’s make sure we know how the coil is oriented in this diagram. In diagram (b), we’re only shown the parts of the coil where the current is traveling into and out of the screen. This corresponds to these edges of the wire, as shown on diagram (a). If we were to add these edges here, onto diagram (b), diagram (b) would end up looking like this.

This makes it much easier to see that in diagram (b) the coil of wire is parallel to the magnetic field. We know that when the coil of wire is parallel to the magnetic field, the magnitude of the potential difference induced across the wire has the maximum value. Of the points marked on this graph, only point 𝑃 corresponds to a potential difference of the maximum value. So, this must be the correct answer to this question.

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