Question

The electrostatic force can be attractive or repelling. How can this be shown numerically?

Answer 1

Electrostatic force sign depends on charge signs: like repels like, opposites attract. Force strength depends on charge magnitudes and distance: bigger charges or closer distance mean stronger force.

The electrostatic force between two charges can be either attractive or repulsive, depending on the charges of the objects. This can be shown numerically using the following equation:

F =
`k * ((q_1 * q_2))/(r^2)`

where:

F is the electrostatic force (in Newtons)

k is Coulomb's constant (approximately 8.998 ×
`10^9 N m^2/C^2`)

q1 is the charge of the first object (in Coulombs)

q2 is the charge of the second object (in Coulombs)

r is the distance between the two objects (in meters)

If both charges are positive or both charges are negative, then the force will be repulsive (positive value). If one charge is positive and the other charge is negative, then the force will be attractive (negative value).

Here are some examples:

Two positive charges (q1 = +1 µC, q2 = +2 µC, r = 1 cm):

F = 8.998 ×
`10^9 N m^2/C^2`* (+1 µC * +2 µC) / (0.01 m)^2

F = 1.7996 ×
`10^(-3)` N (repulsive)

Two negative charges (q1 = -1 µC, q2 = -2 µC, r = 1 cm):

F = 8.998 ×
`10^9 Nm^2/C^2` * (-1 µC * -2 µC) / (0.01 m)^2

F = 1.7996 ×
`10^(-3)` N (repulsive)

One positive charge and one negative charge (q1 = +1 µC, q2 = -2 µC, r = 1 cm):

F = 8.998 ×
`10^9 Nm^2/C^2` * (+1 µC * -2 µC) / (0.01 m)^2

F = -3.5992 ×
`10^(-3)` N (attractive)