Electric Fields of Charge Distributions - AP Physics C: Electricity and Magnetism

$E = \frac{\rho}{3\varepsilon_0} \times r$ (inside sphere). Field from distributed volume charge.

$E = \frac{\sigma}{2\varepsilon_0}$. Field from infinite plane charge.

$E = \frac{1}{4\pi\varepsilon_0} \frac{p}{r^3}$ (perpendicular axis). Dipole field perpendicular to axis.

Simplifies the integration of field contributions. Symmetry simplifies field calculations.

Force per unit charge. Field as force per unit charge.

Radially outward. Field direction from positive charges.

Zero. Equal charges create canceling fields.

Fields from multiple sources add vectorially. Vector addition principle for fields.

$E = \frac{kQ}{r^2}$ (outside), $E = \frac{kQr}{R^3}$ (inside). Different formulas inside and outside sphere.

It is zero. Conductor cavity has no field.

Simplifies the integration of field contributions. Symmetry simplifies field calculations.

Zero. Symmetry cancels field components.

$E = -\nabla V$. Field as negative gradient of potential.

Field increases with charge density. Direct proportionality relationship.

$E = \frac{\sigma}{2\varepsilon_0}$. Field from infinite plane charge.

$E = \frac{\sigma}{\varepsilon_0}$. Surface field on conducting material.

The fields add up. Fields from opposite charges reinforce.

$E = \frac{\lambda}{2\pi\varepsilon_0 r}$. Field from infinite line charge.

The total electric field is the vector sum of individual fields. Individual fields combine vectorially.

The field decreases by a factor of 4. Field follows inverse square law.

$E = \frac{\sigma}{2\varepsilon_0}$. Field from infinite charged sheet.

$F = qE$. Electric force on charge in field.

$E = \frac{\sigma}{2\varepsilon_0}$. Field from uniform surface charge.

Radially inward. Field lines point toward negative charges.

Newton per Coulomb (N/C). SI unit for electric field strength.

Electric force per unit charge. Definition of electric field vector.

$E = \frac{kq}{r^2}$. Coulomb's law for electric field intensity.

Permittivity of free space. Fundamental electromagnetic constant.

Zero. Symmetry cancels all field components.