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| 184_notes:ind_i [2021/06/17 16:25] – [Induced Voltage and the Electric Field] bartonmo | 184_notes:ind_i [2021/06/17 16:28] – bartonmo | ||
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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. | ||
| - | Determining the direction of the induced current just based on the magnetic flux can be tricky because there are a lot of different parts to the equation. In the next page of notes, we will walk through a new right hand rule for the induced current step-by-step. | + | Determining the direction of the induced current just based on the magnetic flux can be tricky because there are a lot of different parts to the equation. In the next page of notes, we will walk through a **new right hand rule** for the induced current step-by-step. |
| /* For this right hand rule, you want to first point your right thumb in the direction of the change in magnetic flux. For our example, the change in magnetic flux would point into the page. (Because $\Delta \Phi_{B}= \Phi_{Bf}-\Phi_{Bi}$, | /* For this right hand rule, you want to first point your right thumb in the direction of the change in magnetic flux. For our example, the change in magnetic flux would point into the page. (Because $\Delta \Phi_{B}= \Phi_{Bf}-\Phi_{Bi}$, | ||