| Coulomb’s law |
$ F=\frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{r^2} $ |
Force between two point charges$ (Q_1,Q_2) $ separated by a distance $r$ |
| Electric potential |
$ V=\sum_{i=1}^N\frac{1}{4\pi\epsilon_0}\frac{Q_i}{r_i} $ |
Work done to bring a positive test charge $q_0$ from infinity to a point $P$ in the electric field created by multiple charges $ Q_i$ |
| Electric potential due to a point charge |
$ V=\frac{1}{4\pi\epsilon_0}\frac{Q}{r} $ |
Electric potential due to a point charge $Q$ at a distance $r$ |
| Electric potential due to a dipole** |
$ V=\frac{1}{4\pi\epsilon_0}\frac{p\cos\theta}{r^2}$ |
Electric potential due to a dipole with dipole moment $(p)$ at a distance $r$ and angle $\theta$ from the dipole axis |
| Electric potential due to a uniformly charged sphere |
$ V=\frac{1}{4\pi\epsilon_0}\left[\frac{3Q}{2R}\right]$, $r>R$ |
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| $ V=\frac{1}{4\pi\epsilon_0}\frac{Q}{2R} $, $r<R$, |
Electric potential due to a uniformly charged sphere with total charge $Q$, radius $R$, and charge density $\rho$. For points outside the sphere $ (r>R)$, the potential is the same as that of a point charge $Q$ located at the center of the sphere. |
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| Electric potential due to a uniformly charged thin rod |
$ V=\frac{1}{4\pi\epsilon_0}\int_{-L/2}^{L/2}\frac{2\lambda}{\sqrt{r^2+x^2}}\text{d}x $ |
Electric potential at point P on the perpendicular bisector of a uniformly charged thin rod of length $L$ and linear charge density $\lambda$. |
| Electric potential due to a uniformly charged infinite plane |
$ V=\frac{\sigma}{2\epsilon_0} $ |
Electric potential due to a uniformly charged infinite plane with charge density $\sigma$ |
BETA
