| Coulomb’s law |
( V=\frac{1}{4\pi\epsilon_0}\frac{Q}{r} ) |
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{2p\cos\theta}{r^2}) |
Electric potential due to a dipole with dipole moment ((2p)) 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}-\frac{\rho r^2}{2\epsilon_0}\right]), (r>R) |
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| ( V=\frac{1}{4\pi\epsilon_0}\frac{3Q}{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) |
