Chapter 11 – Electrostatics (Physics)
1. Electric Charge
Electric charge is a fundamental property of matter responsible for electrical interactions.
There are two types of charges:
- Positive charge
- Negative charge
Like charges repel each other, unlike charges attract each other.
2. Quantization of Charge
$q = ne$
- $e = 1.6 \times 10^{-19}\,\text{C}$
- $n$ is an integer
3. Conservation of Charge
Total electric charge of an isolated system remains constant.
Charge can neither be created nor destroyed.
4. Coulomb’s Law
The force between two point charges is directly proportional to the product of charges
and inversely proportional to the square of distance between them.
$F = k \dfrac{q_1 q_2}{r^2}$
$k = \dfrac{1}{4\pi\varepsilon_0}$
5. Vector Form of Coulomb’s Law
$\vec{F}_{12} = \dfrac{1}{4\pi\varepsilon_0}
\dfrac{q_1 q_2}{r^2}\hat{r}_{12}$
6. Principle of Superposition
The net force on a charge due to multiple charges is the vector sum
of forces due to individual charges.
7. Electric Field
Electric field is defined as force per unit positive test charge.
$\vec{E} = \dfrac{\vec{F}}{q}$
8. Electric Field Due to a Point Charge
$E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}$
9. Electric Field Lines
- Field lines start from positive charge
- Field lines end on negative charge
- Field lines never intersect
10. Electric Dipole
An electric dipole consists of two equal and opposite charges separated by a small distance.
$\vec{p} = q \vec{d}$
11. Electric Field Due to Dipole (Axial & Equatorial)
$E_{\text{axial}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^3}$
$E_{\text{equatorial}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^3}$
12. Torque on Electric Dipole
$\tau = pE\sin\theta$
13. Electric Flux
$\Phi_E = \vec{E} \cdot \vec{A}$
14. Gauss’s Law
$\oint \vec{E}\cdot d\vec{A} = \dfrac{q_{\text{enc}}}{\varepsilon_0}$
15. Applications of Gauss’s Law
- Electric field due to infinite line charge
- Electric field due to infinite plane sheet
- Electric field due to spherical shell
16. Electric Potential
Electric potential at a point is the work done per unit charge
in bringing a test charge from infinity to that point.
$V = \dfrac{W}{q}$
17. Electric Potential Due to Point Charge
$V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$
18. Relation Between Electric Field and Potential
$\vec{E} = -\nabla V$
19. Equipotential Surfaces
- Electric field is perpendicular to equipotential surface
- No work is done along equipotential surface
20. Capacitance
$C = \dfrac{Q}{V}$
21. Parallel Plate Capacitor
$C = \dfrac{\varepsilon_0 A}{d}$
22. Energy Stored in Capacitor
$U = \dfrac{1}{2}CV^2$
23. Dielectric and Relative Permittivity
$\varepsilon = \varepsilon_0 K$
24. Series and Parallel Combination of Capacitors
$\dfrac{1}{C_s} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$
$C_p = C_1 + C_2$
25. Final Revision Checklist
You have mastered Electrostatics if you can:
- Apply Coulomb’s law in vector form
- Calculate electric field using Gauss law
- Relate electric field and potential
- Solve capacitor problems confidently