Answer to Question #133107 in Electricity and Magnetism for alfraid

Question

write formula electric field due to point charge.

Answer 1

Let the point charge be Q. Next, we may put a charge q to the point with distance r from Q. Therefore, the electric force will be

$F=k\cdot\dfrac{Qq} {r^2} .$ Here k is a constant equal to $9\cdot10^9\mathrm{Nm^2/C^2}.$

The modulus of the electric field is

$E=\dfrac{F} {q} =k\cdot \dfrac{Q} {r^2}$

The direction of the field is towards the vector from Q if it is positive and to Q if it is negative.

So we may rewrite it as

$\vec{E} =k\cdot\dfrac{Q} {r^3} \cdot\vec{r}.$

In case of non-vacuum, we should add a factor $\varepsilon$

$\vec{E} =k\cdot\dfrac{Q} {\varepsilon r^3} \cdot\vec{r}.$