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

2024
Views:

485

Pages:

2
Author:

Jabin F.

# Electric potential and field of electric dipole:- Nat(te) e) few A P 0 axis of dipole 2 law of \[\begin{matrix}V=&\frac{1}{4\pi\epsilon_{0}}[\frac{q}{\gamma_{+}}-\frac{2}{\gamma_{-}}]-\cdot\cdot\cdot(i)\\ r_{asines\rightarrow\end{matrix}\] += 2²+(일)2=2(일)rwe (der \[\gamma_{c}=\int\gamma^{2}+(\frac{\phi}{z})^{2}+2(\frac{\phi}{z})r~los~\Theta\] ⇒ \(\gamma_{+}=\int\gamma_{-}^{1}d\gamma~cos~\theta)^{\gamma_{r_{-...}}\) \[\gamma_{-}=(\begin{matrix}\gamma_{+}^{2}dr~Lod\theta)^{\gamma_{\gamma}.}\] \[\gamma_{+}=\gamma(1-\frac{d}{\gamma}log~\theta)^{1/2}\] \[r_{-}=r(1+\frac{d}{r}.cos~\theta)^{1/2}\] ↓ \(\frac{i}{\gamma_{+}}_{*}=\frac{i}{\gamma}(i-\frac{\alpha}{\gamma}.\zeta_{4}\theta)^{-\frac{1}{2}}\) muni By bineminel =÷(1+1)-) \[\frac{1}{\gamma_{+}}=\frac{1}{\gamma}(1+\frac{d}{\gamma}cos~\theta)^{-\frac{1}{2}}\] \[\begin{matrix}=&\frac{1}{\gamma}(1-\frac{d}{\gamma}cos~\theta)-\cdot\cdot\cdot(iii)\\ from\\ previous\\ page\end{matrix}\] from (ii) and (iii) Put in (i) \[V=\frac{qd\cos\theta}{4\pi\epsilon_{0}r^{2}}-\cdot\cdot\cdot(iv)\] \[V\propto\frac{\cos\theta}{r^{2}}-\cdot\cdot\cdot(v)\] from previous page \[\begin{matrix}\checkmark monopole=&\frac{q}{4\pi\epsilon_{0}r}\\\checkmark dipole=&\frac{qd\cos\theta}{4\pi\epsilon_{0}r^{2}}\end{matrix}\]