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:

Uniformly distributed charge along a line

: Charge per unit length

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

A plane of charge

: Charge per unit area

For a uniformly charged ring

: Total charge

A semi-circle

: Charge per unit length

A uniformly charged disk

: Charge per unit area

The infinite plane

A parallel-plate capacitor

: Charge per unit area

Electric Dipoles

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

Dipole moment:

Dipole in external field
  1. Total force
  2. Torque on the dipole

Field Lines

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.

Uniform field

In uniform field:

General cases

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

A spherical shell

Outside the shell:

Inside the shell:

Same for a uniformly charged conductor sphere

A uniformly charged nonconducting 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:

Field created by a point charge

Charged conductor sphere
  1. : Same as point charge,
  2. : Same potential at any point,
Uniformly charged rod

Uniformly charged ring

Determine from :


Capacitance of capacitor:

A parallel-plate capacitor

Cylindrical capacitor

Capacitors in series

Capacitors in parallel

Electric energy stored:

Energy per unit volume / Energy density:


Capacitor compeletely filled by a deilectric

Dielectric: Insulating material in capacitors.

  1. Harder to break down: Increase .
  2. Less equivlant distance between plates.
  3. Increase the capacitance:

Dielectric constant : also noted as , relative permittivity.

The permittivity of material:

Energy density in a dielectric: