Coulomb's Law

The Magnitude of Electrical Force calculator uses Coulomb's Law to compute the electrical force between two objects based on their charge, the distance between them and Coulomb’s Constant.

INSTRUCTIONS: Choose units and enter the following:

• (q₁) Charge of body 1
• (q₂ )Charge of body 2
• (r) Separation Distance

Magnitude of Electrical Force |K|: The force is returned in Newtons.  However, this can be automatically converted to compatible units via the pull-down menu.
 

The Math / Science

The magnitude of the electrical force acting between point-like charged objects at a center-to-center distance `r` is given by the equation  

         `|K| = k(|q_1||q_2|)/(r^2)`

where:

• |K| = Magnitude of electrical force
• k = 9.0×10⁹ N?m²/C² (Coulomb’s Constant)
•  q₁ = Charge of body 1
•  q₂ = Charge of body 2
•  r = separation distance

The force is attractive if the charges are of different signs, and repulsive if they have the same sign.

Note that Coulomb's law is closely analogous to Newton's law of the force of gravity, where the magnitude of the force is `Gm_1m_2"/"r^2`, except that there is only one type of mass, not two, and gravitational forces are never repulsive. Because of this close analogy between the two types of forces, we can recycle a great deal of our knowledge of gravitational forces. For instance, there is an electrical equivalent of the shell theorem: the electrical forces exerted externally by a uniformly charged spherical shell are the same as if all the charge was concentrated at its center, and the forces exerted internally are zero.

References

21.2 Electrical forces by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.