Class 12 Physics - Electric Charges and Fields

Electrostatics deals with the study of forces, fields, and potentials arising from static charges.

1. Coulomb's Law

The force of attraction or repulsion between two point charges $q_1$ and $q_2$ is: $F = k \cdot \frac{|q_1 q_2|}{r^2}$ where $k = \frac{1}{4\pi\varepsilon_0} \approx 9 \times 10^9 \text{ Nm}^2\text{C}^{-2}$.

2. Electric Field (E)

Electric field intensity at a point is the force experienced by a unit positive charge placed at that point. $E = \frac{F}{q_0}$

• For a point charge: $E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q}{r^2}$

3. Electric Dipole

A pair of equal and opposite charges separated by a small distance $2a$. Dipole Moment ($p$) = $q \times 2a$ (Directed from $-q$ to $+q$).

• Field on Axis: $E = \frac{2kp}{r^3}$
• Field on Equator: $E = \frac{kp}{r^3}$

4. Electric Flux ($\Phi$)

Total number of electric field lines passing through a given area. $\Phi = \int E \cdot dA = E A \cos\theta$

5. Gauss's Law

The total electric flux through any closed surface is equal to $1/\varepsilon_0$ times the net charge enclosed by the surface. $\oint E \cdot dS = \frac{q_{enclosed}}{\varepsilon_0}$

💡 Key Applications of Gauss's Law

1. Field due to an infinitely long straight wire: $E = \frac{\lambda}{2\pi\varepsilon_0 r}$
2. Field due to a uniformly charged infinite plane sheet: $E = \frac{\sigma}{2\varepsilon_0}$

Derivations are very important for Boards! ⚡