Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
| 184_notes:examples:week7_cylindrical_capacitor [2018/06/19 15:37] – curdemma | 184_notes:examples:week7_cylindrical_capacitor [2021/06/15 13:52] (current) – schram45 | ||
|---|---|---|---|
| Line 11: | Line 11: | ||
| ===Lacking=== | ===Lacking=== | ||
| * Capacitance | * Capacitance | ||
| - | |||
| - | ===Approximations & Assumptions=== | ||
| - | * The cylinders are much longer than they are far from one another, i.e., L>>a,b. | ||
| - | * Cylinders are uniformly charged. | ||
| ===Representations=== | ===Representations=== | ||
| Line 46: | Line 42: | ||
| & | & | ||
| \end{align*} | \end{align*} | ||
| + | |||
| + | <WRAP TIP> | ||
| + | ===Approximations & Assumptions=== | ||
| + | In order to take the electric field term out of the integral there are two assumptions that must be made. | ||
| + | * The charge is uniformly distributed amongst the cylindrical plates: Any charge concentrations would create inconsistencies in the electric field from the charges cylinders. This is a good assumption for highly conductive plate materials. | ||
| + | * The length of the cylinders is much greater than how far they are apart: This allows the electric field to be constant along the length of the cylinder at a given radius so long as the last assumption also holds. | ||
| + | </ | ||
| The last thing we need is Qenclosed. This is simply the fraction of Q that the Gaussian surface encloses. Since the height of the Gaussian cylinder is h, we have Qenclosed=hLQ. We can now write the magnitude of the electric field at a radius s from the central vertical axis (given that a<s<b). | The last thing we need is Qenclosed. This is simply the fraction of Q that the Gaussian surface encloses. Since the height of the Gaussian cylinder is h, we have Qenclosed=hLQ. We can now write the magnitude of the electric field at a radius s from the central vertical axis (given that a<s<b). | ||