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| 184_notes:examples:week14_changing_current_rectangle [2018/08/09 19:14] – curdemma | 184_notes:examples:week14_changing_current_rectangle [2021/07/13 13:26] (current) – [Solution] schram45 | ||
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| ===Approximations & Assumptions=== | ===Approximations & Assumptions=== | ||
| - | * The long wire is infinitely long and thin and straight. | + | * The long wire is infinitely long and thin and straight: With these assumptions the magnetic field produced by the wire only depends on the radial distance away from the wire and the current in it. This also allows us to use a simplified magnetic field equation from the notes. |
| - | * There are no external contributions to the B-field. | + | * There are no external contributions to the B-field: We are not told about any other external moving charges or currents that could also produce a magnetic field that would effect the flux through our loop, so we will assume the only contribution is from the long wire. |
| ===Representations=== | ===Representations=== | ||
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| [{{ 184_notes: | [{{ 184_notes: | ||
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| + | The induced voltage in this problem was a constant, which means the flux must be changing linearly with time. Thats the only way the derivative can be a constant. If we look at the equation for flux through a loop there are three ways it can change. The first is if the magnetic field changes, the second is if the cross product changes, and the third is if the area changes with time. None of the sides of our loop are moving, so the area is not changing with time. The relationship of our magnetic field and area vector are also not changing as our loop is not rotating and our magnetic field is always in the same direction. This leaves the magnetic field, which is changing in this example. The magnetic field in this problem changes just like the current in the long wire. Since the current in the long wire changes linearly with time, our flux must change linearly with time as well. This means our induced voltage should be a constant as our solution shows. | ||