Electrostatic force between two charges

Also known as Coulomb’s law, it is an experimental law that calculates the amount of force between two electrically charged particles at rest.

Also see the scalar law.

Notes:

1. If a given charge is in the vicinity of a system of point charges, then the net law can be found via the principle of superposition.

Notation:

1. \(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.

Conditions:

1. The charges are small.

2. The charges are at rest.

Links:

1. Wikipedia.

force

Vector of the electrostatic force experienced by the first_charge in the vicinity of the second_charge in vacuum.

Symbol:

F_12

Latex:

\({\vec F}_{12}\)

Dimension:

force

first_charge

Value of the first point charge.

Symbol:

q_1

Latex:

\(q_{1}\)

Dimension:

charge

second_charge

Value of the second point charge.

Symbol:

q_2

Latex:

\(q_{2}\)

Dimension:

charge

position_vector

Position vector drawn from the second_charge to the first_charge.

Symbol:

d_21

Latex:

\({\vec d}_{21}\)

Dimension:

length

force_law

F_12 = q_1 * q_2 / (4 * pi * epsilon_0) * d_21 / norm(d_21)^3

Latex:

\[{\vec F}_{12} = \frac{q_{1} q_{2}}{4 \pi \varepsilon_0} \frac{{\vec d}_{21}}{\left \Vert {\vec d}_{21} \right \Vert^{3}}\]

position_vector_law

d_21 = sign(q_1 * q_2) * sqrt(Abs(q_1 * q_2) / (4 * pi * epsilon_0)) * F_12 / norm(F_12)^(3/2)

Latex:

\[{\vec d}_{21} = \operatorname{sign}{\left(q_{1} q_{2} \right)} \sqrt{\frac{\left|{q_{1} q_{2}}\right|}{4 \pi \varepsilon_0}} \frac{{\vec F}_{12}}{\left \Vert {\vec F}_{12} \right \Vert^{\frac{3}{2}}}\]