CBSE · Class 12 · Physics · Electric Charges and FieldsState Coulomb's inverse square law in electrostatics. State the factors on which electrostatic force depends and express the law in vector form.

Coulomb's Inverse Square Law

Statement: According to Coulomb's Law, the force of attraction or repulsion between two stationary point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This force acts along the straight line joining the centers of the two charges.

Mathematical Form: $$F = \frac{1}{4\pi\varepsilon_0 \varepsilon_r} \frac{|q_1 q_2|}{r^2}$$

Factors Affecting Electrostatic Force:

1. Magnitude of Charges ($q_1, q_2$): Force is directly proportional to product of charges ($F \propto |q_1 q_2|$).
2. Distance ($r$): Force is inversely proportional to square of distance ($F \propto \frac{1}{r^2}$).
3. Medium: Force depends on dielectric constant ($K$ or $\varepsilon_r$) of surrounding medium ($F \propto \frac{1}{\varepsilon_r}$). In a dielectric medium, force decreases.

Vector Form:\nForce exerted on charge $q_1$ by $q_2$ is:

$$\vec{F}{12} = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2} \hat{r}{21}$$\nwhere $\hat{r}_{21}$ is a unit vector pointing from charge $q_2$ to charge $q_1$.