# Physics Speedrun - Electric Field

## Electric Charge

1. Two types: positive, negative
2. Quantized:
3. Conserved.

## Coulomb's Law

Premittivity of free space

## Electric Field

For a point charge:

: Charge per unit length

Notice that is defined as the outer angle. When it is infinitly long, ,

: Charge per unit area

: Total charge

: Charge per unit length

: Charge per unit area

The infinite plane

: Charge per unit area

### Electric Dipoles

Combination of two equal charges of opposite charges is called an electric dipole.

Dipole moment:

1. Total force
2. Torque on the dipole

### Field Lines

1. The field point is in the direction tangent to the field line.
2. Magnitude of numbers of lines crossing unit area the lines.
3. Starts on + charges, ends on - charges.
4. Never cross. Never closed.

### Electric Flux

: Electirc flux through an area numbers of field lines passing that area.

In uniform field:

General cases:

For a closed surface, define outward as positive, the net flux:

### Gauss's Law

The Gauss's law:

Differential form:

Useful when the charge distribution is highly symmetric, may determine the magnitude of electric field by

On a proper Gaussian surface, there must be

Outside the shell:

Inside the shell:

Same for a uniformly charged conductor sphere

Outside the shell:

Inside the shell: In a hole in a uniformly charged sphere, the electric field is uniform Proper Gaussian surface for an infinitly long cylinder

Conductor in external field

When in electorstatic equilibrium:

1. Inside:
2. On surface:

Charge tends to concentrate on surface with greater curvature.

## Electric Potential

Coulomb force is conservative. .

Potential energy :

Electric potential:

Potential difference / voltage:

Usually let at infinity:

1. : Same as point charge,
2. : Same potential at any point,

Determine from :

## Capacitors

Capacitance of capacitor:

Electric energy stored:

Energy per unit volume / Energy density: