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184_notes:examples:week4_charge_ring [2021/05/25 14:35] – schram45 | 184_notes:examples:week4_charge_ring [2021/05/25 14:38] (current) – schram45 | ||
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We can represent the ring and P as follows, with coordinates chosen conveniently. We choose cylindrical coordinates because we will be integrating over the length of the ring, and being able to represent its radius as constant will simplify calculations. | We can represent the ring and P as follows, with coordinates chosen conveniently. We choose cylindrical coordinates because we will be integrating over the length of the ring, and being able to represent its radius as constant will simplify calculations. | ||
{{ 184_notes: | {{ 184_notes: | ||
- | |||
- | <WRAP TIP> | ||
- | ===Approximation=== | ||
- | The ring is in a perfect circle. | ||
- | </ | ||
====Solution==== | ====Solution==== | ||
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We begin with an approximation, | We begin with an approximation, | ||
* The thickness of the ring is infinitesimally small, and we can approximate it as a circle. | * The thickness of the ring is infinitesimally small, and we can approximate it as a circle. | ||
+ | * The ring is in a perfect circle. | ||
</ | </ | ||
We also make a plan to tackle the integrating, | We also make a plan to tackle the integrating, | ||
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<WRAP TIP> | <WRAP TIP> | ||
===Assumption=== | ===Assumption=== | ||
- | The charge is evenly distributed along the ring. This also assumes the ring is a perfect conductor where charges will distribute evenly along the conductor. | + | The charge is evenly distributed along the ring. This also assumes the ring is a perfect conductor where charges will distribute evenly along the conductor. If this were not true, the charge density along the ring would not be constant. |
</ | </ | ||