Comparing the equations for the gravitational and electric force

$$\vec{F}_g=-\frac{Gm_1m_2}{r^2}$$ and $$\vec{F}_e=\frac{Kq_1q_2}{r^2}$$

I noticed the only major difference between them is that the constant $K$ depends on the medium. Why does it?


2 Answers 2


First remember that $k = \dfrac {1}{4 \pi \epsilon_r\epsilon_o}$ where $\epsilon_r \ge 1$

It is because a medium can be polarised by an external E-field.
The dipoles so set up produce the external E-field produce an E-field in the opposite direction so the net E-field (the sum of the external and dipole produced E-fields) is smaller.
Thus the force a given charge is smaller.

enter image description here

A metal is "perfect" at negating the external E-field, so much so that the E-field in a metal is zero.

  • 9
    $\begingroup$ and gravitational force till now showed no such polarisation of matter. $\endgroup$ Feb 6, 2016 at 12:01
  • 2
    $\begingroup$ I love these diagrams of yours... $\endgroup$
    – manshu
    Feb 6, 2016 at 15:30
  • $\begingroup$ Are we talking about static fields here? Would a time-varying field matter? $\endgroup$ Feb 7, 2016 at 2:12
  • $\begingroup$ I wrote the answer with static charges in mind but metals can have E-fields within them; that is the reason for electric currents flowing. The reduction in E-field in a medium is the reason for the capacitance of a capacitor increasing when a dielectric is introduced and this effect is relevant in ac circuits. $\endgroup$
    – Farcher
    Feb 7, 2016 at 7:05

In electromagnetism there are both positive and negative charges. Hence the force due to electric charges can be attractive or repulsive. Gravity, when treated as a classical force field, can only be attractive, there are not two types of "gravitational charge".

What this means is that in electromagnetism, a given medium, may contain both positive and negative charges and these can be separated by the application of an electric field - a process called polarisation. The separation of the electric charges produces an electric field that when summed with the applied electric field leads to a different net electric field in the medium and thus a different force acting on a test charge in the medium.

Since there is only one type of "gravitational charge", this phenomenon does not occur when applying a gravitational field.


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