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| 184_notes:ind_i [2021/06/17 16:14] – [Why do we need the negative sign?] bartonmo | 184_notes:ind_i [2021/06/17 16:21] – [Why do we need the negative sign?] bartonmo | ||
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| As an example of how to figure out which direction the induced current flows, let's say we have a bar that is sliding down a pair of connected conductive rails (so current is free to flow through the loop created by the bar and rails), which is sitting in a magnetic field that points into the page (shown in the top figure to the right). Initially there would be some magnetic flux through the loop. At a later time (shown in the second picture to the right), after the bar has moved down the rails, there would be a larger magnetic flux through the loop because the area of the loop will have increased. Since the magnetic flux increased, we know that there should be an induced current in the loop - but what direction should it flow around the loop? | As an example of how to figure out which direction the induced current flows, let's say we have a bar that is sliding down a pair of connected conductive rails (so current is free to flow through the loop created by the bar and rails), which is sitting in a magnetic field that points into the page (shown in the top figure to the right). Initially there would be some magnetic flux through the loop. At a later time (shown in the second picture to the right), after the bar has moved down the rails, there would be a larger magnetic flux through the loop because the area of the loop will have increased. Since the magnetic flux increased, we know that there should be an induced current in the loop - but what direction should it flow around the loop? | ||
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| Let's suppose that the induced current flows counter-clockwise in the loop (shown in the figure above). If we use our original right hand rule for magnetic force ($\vec{F} = \int I d\vec{l} \times \vec{B}$), we should get a force on the bar that points in the negative x-direction. This means that the magnetic force on the induce current would act to //slow down// the moving bar. With the bar slowing down, this is actually good for energy conservation. It means that we have to put energy into the system to keep the bar moving, and in turn that mechanical energy is turned into electrical energy by inducing a current. If you stopped moving the moving the bar, it would eventually slow down and come to rest. This tells us by energy conservation - the induced current should flow counter-clockwise around the loop. If we had instead hypothesized that the induced current flowed in a clockwise direction, we would instead get a force in the +x direction. This would mean that the bar would continually speed up, which induces more current, which then causes the bar to speed up even more! This would completely break energy conservation and mean that you are essentially creating energy out of nothing. This simply cannot happen. So we know that the induced current must be counter-clockwise in our loop. | Let's suppose that the induced current flows counter-clockwise in the loop (shown in the figure above). If we use our original right hand rule for magnetic force ($\vec{F} = \int I d\vec{l} \times \vec{B}$), we should get a force on the bar that points in the negative x-direction. This means that the magnetic force on the induce current would act to //slow down// the moving bar. With the bar slowing down, this is actually good for energy conservation. It means that we have to put energy into the system to keep the bar moving, and in turn that mechanical energy is turned into electrical energy by inducing a current. If you stopped moving the moving the bar, it would eventually slow down and come to rest. This tells us by energy conservation - the induced current should flow counter-clockwise around the loop. If we had instead hypothesized that the induced current flowed in a clockwise direction, we would instead get a force in the +x direction. This would mean that the bar would continually speed up, which induces more current, which then causes the bar to speed up even more! This would completely break energy conservation and mean that you are essentially creating energy out of nothing. This simply cannot happen. So we know that the induced current must be counter-clockwise in our loop. | ||