# Electrostatics formulas

## Electrostatic force

### Coulomb's Law

F = kq1q2/r2

where k=1/4πεo=9x109Nm2C-2

εo = 8.85x10-12C2m-2N-1

See a solved example at Buzztutor.com

### Vector notation  ## Electrostatic field

### Electric field due to a point charge

E = F/qo = kq/r2 N/C

See a solved example at Buzztutor.com

E due to circular loop of charge (radius r) at a distance x from the center ## Electric dipole

### Dipole moment Cm

### Electric field at an axial point of a dipole ### Electric field at an equatorial point of a dipole ### Torque acting on a dipole in a uniform electric field ### Potential energy of a dipole in a uniform electric field  ## Electrostatic potential

### Electrostatic potential difference ### Potential due to a point charge ### Potential at an axial point of a dipole if then ### Potential at an equatorial point of a dipole ## Relation between electrostatic field and potential gradient

### Electric field = negative of the potential gradient ## Electrostatic potential energy

### Electrostatic potential energy of two point charges ## Gauss' theorem

### Electric flux ### Gauss' theorem Definition: Electric flux ϕ through any closed surface is 1/εo times the net charge Q enclosed by the surface.

### Electric field E due to infinitely long straight wire (a line charge) ### Electric field E due to thin infinite plane sheet of charge ### Electric field between two thin infinite plane parallel sheets of charge ### Electric field due to uniformly charged spherical shell for r > R for r < R for r = R

## Capacitance Farad 1F = 1 C/V

### Isolated spherical conductor ### Parallel plate capacitor or where and k is dielectric constant

### Capacitors in series ### Capacitors in parallel ### Energy stored in a capacitor Energy density ### Common potential ### C with conducting slab between the two plates where t is thickness of slab [t < d]

### C with dielectric slab between the two plates where k is the dielectric constant