MHB Electrostatic Force: Effects of Distance

[Dustinsfl]

How does electrostatic force vary between two objects if the distance is doubled?

I know with gravitational force as the distance doubles the force decreases by \(\frac{1}{4}\).

 

[Chris L T521]

How does electrostatic force vary between two objects if the distance is doubled?

I know with gravitational force as the distance doubles the force decreases by \(\frac{1}{4}\).

Gravitational and Electrostatic force fields are both inverse square fields. In particular for gravity (known as Newton's Law of Universal Gravitation),

\[F_g = G\frac{m_1m_2}{d^2}\]

where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of objects and $d$ is the distance between these two objects.

Likewise for electrostatic force (known as Coulomb's Law),

\[F_e = k_e\frac{|q_1q_2|}{d^2}\]

where $k_e$ is Coulomb's constant, $q_1$ and $q_2$ are the signed charges of the particles, and $d$ is the distance between these two particles.

So if the distance between any two particles/objects is doubled in either case, the force decreases by a factor of $\dfrac{1}{4}$.