Potential | Santa Fe College - Edubirdie

University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

430

Pages:

2
Author:

Jabin F.

Potential → dU = -Fdr = -qEdr Vin = -\int_{0}^{R} Edr Vin = -\frac{2}{4π\epsilon₀} \int_{0}^{R} \frac{dr}{r²} - \frac{2Y}{4π\epsilon₀R³} \int_{0}^{R} rdr Vin = -\frac{2}{4π\epsilon₀} [\frac{-1}{r}]{0}^{R} - \frac{2Y}{4π\epsilon₀R³} [\frac{r²}{2}]{0}^{R} Vin = \frac{2}{4π\epsilon₀R} - \frac{1}{4π\epsilon₀R³} [\frac{r²}{2} - \frac{R²}{2}] Vin = \frac{2}{4π\epsilon₀R} - \frac{2r²}{4π\epsilon₀R³ \times 2} + \frac{2}{4π\epsilon₀Rx₂} Vin = \frac{9(3R² - γ²)}{8π\epsilon₀R³} V_{centre} = \frac{9}{8π\epsilon₀R} V_{surface} = \frac{9}{4π\epsilon₀R} V_{r=0} = \frac{9}{8π\epsilon₀R} V_{r=R} = \frac{9}{4π\epsilon₀R} V_{out} = -\int_{\infty} E_{out} dr = \frac{q}{4π\epsilon₀R}

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