- लगभग 600 ईसा पूर्व (BC) में, यूनान के दार्शनिक थेल्स (Thales) ने देखा कि जब अम्बर (Amber) को बिल्ली की खाल से रगड़ा जाता है; तो उसमें कागज के छोटे-छोटे टुकड़े आदि को आकर्षित करने का गुण आ जाता है ।
- Charges :
- आवेशों के लिए ऋणात्मक एवं धनात्मक पदों का प्रयोग सर्वप्रथम बेंजामिन फ्रेंकलिन (Benjamin Franklin) ने किया था ।
- Negative charge
- Positive charge
- like charges – Repel
- Unlike charges- Attraction
Electrostatics Quick Revision Notes
Exam Focus: These notes cover key concepts frequently tested in SSC CGL, UPSC, and other competitive exams.
1. Electric Charge
- Charge is quantized: \( q = ne \), where \( n = \pm 1, \pm 2, \pm 3, \ldots \) and \( e = 1.6 \times 10^{-19} \, \text{C} \)
- Like charges repel, unlike charges attract
- Conservation of charge: Total charge in an isolated system remains constant
2. Coulomb’s Law
The force between two point charges:
\[ F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \]
where \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)
\[ F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \]
where \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)
- Force is conservative, central, and obeys Newton’s third law
- In vector form: \( \vec{F} = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \hat{r} \)
3. Electric Field
Electric field due to a point charge:
\[ \vec{E} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \hat{r} \]
\[ \vec{E} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \hat{r} \]
- Field lines start from positive charges and end at negative charges
- Number of field lines is proportional to the magnitude of charge
- Field lines never intersect
4. Electric Flux
\[ \Phi = \int \vec{E} \cdot d\vec{A} \]
For uniform field and flat surface: \( \Phi = E A \cos\theta \)
For uniform field and flat surface: \( \Phi = E A \cos\theta \)
5. Gauss’s Law
\[ \oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enc}}}{\epsilon_0} \]
- Applicable to closed surfaces (Gaussian surfaces)
- Useful for calculating E for symmetric charge distributions
6. Applications of Gauss’s Law
Infinite straight wire: \( E = \frac{\lambda}{2\pi\epsilon_0 r} \)
Infinite plane sheet: \( E = \frac{\sigma}{2\epsilon_0} \)
Spherical shell:
– Inside: \( E = 0 \)
– Outside: \( E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \)
Solid sphere:
– Inside: \( E = \frac{1}{4\pi\epsilon_0} \frac{qr}{R^3} \)
– Outside: \( E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \)
Infinite plane sheet: \( E = \frac{\sigma}{2\epsilon_0} \)
Spherical shell:
– Inside: \( E = 0 \)
– Outside: \( E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \)
Solid sphere:
– Inside: \( E = \frac{1}{4\pi\epsilon_0} \frac{qr}{R^3} \)
– Outside: \( E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \)
7. Electric Potential
Potential difference: \( V_B – V_A = -\int_A^B \vec{E} \cdot d\vec{l} \)
Potential due to point charge: \( V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} \)
Potential due to point charge: \( V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} \)
- Potential is scalar, while field is vector
- Equipotential surfaces are perpendicular to field lines
8. Capacitance
\[ C = \frac{Q}{V} \]
Parallel plate capacitor: \( C = \frac{\epsilon_0 A}{d} \)
Spherical capacitor: \( C = 4\pi\epsilon_0 \frac{ab}{b-a} \)
Isolated sphere: \( C = 4\pi\epsilon_0 R \)
Parallel plate capacitor: \( C = \frac{\epsilon_0 A}{d} \)
Spherical capacitor: \( C = 4\pi\epsilon_0 \frac{ab}{b-a} \)
Isolated sphere: \( C = 4\pi\epsilon_0 R \)
9. Capacitors in Circuits
Series: \( \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots \)
Parallel: \( C_{\text{eq}} = C_1 + C_2 + C_3 + \cdots \)
Parallel: \( C_{\text{eq}} = C_1 + C_2 + C_3 + \cdots \)
10. Energy in Capacitors
\[ U = \frac{1}{2} CV^2 = \frac{1}{2} QV = \frac{Q^2}{2C} \]
Energy density: \( u = \frac{1}{2} \epsilon_0 E^2 \)
Energy density: \( u = \frac{1}{2} \epsilon_0 E^2 \)
11. Dielectrics
- Dielectric constant: \( K = \frac{C}{C_0} \)
- Polarization reduces effective field: \( E = \frac{E_0}{K} \)
- Capacitance with dielectric: \( C = KC_0 \)
Important Formulas Summary
| Concept | Formula |
|---|---|
| Coulomb’s Law | \( F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \) |
| Electric Field (Point Charge) | \( E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \) |
| Electric Flux | \( \Phi = EA\cos\theta \) |
| Gauss’s Law | \( \oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enc}}}{\epsilon_0} \) |
| Electric Potential (Point Charge) | \( V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} \) |
| Potential Difference | \( V_B – V_A = -\int_A^B \vec{E} \cdot d\vec{l} \) |
| Capacitance | \( C = \frac{Q}{V} \) |
| Parallel Plate Capacitor | \( C = \frac{\epsilon_0 A}{d} \) |
| Energy in Capacitor | \( U = \frac{1}{2} CV^2 = \frac{1}{2} QV = \frac{Q^2}{2C} \) |
Important Constants
| Constant | Value |
|---|---|
| Charge of electron (e) | \( -1.6 \times 10^{-19} \, \text{C} \) |
| Permittivity of free space (ε₀) | \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \) |
| \( \frac{1}{4\pi\epsilon_0} \) | \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \) |
- Electric field
- Electric lines of force
- Conductor
- Non-conductor
- Semi-conductor
- Surface density of charge
- Laws of Electric Force or Coulomb’s Law
- Permitivity
- Electric Field
- Electric Force
- Intensity of Electric Field
- Electric Potential
- Electric Field Lines
- Electric Flux
- Electric Dipole
- Capacitor
- Dielectric
- Electric Current
- Electric Current Density
- Ohm’s Law
- Conductivity
- Superconductor
- Conductance
- Electric Cell
- Primary
- Secondary
- EMF Vs Potential Difference
- Kirchoff’s Law
- Electric Power
- Joules Law Of Heating
- Wheatstone Bridge
- Meter Bridge
- Potentiometer
- Cyclotron
- Galvanometer
- Voltmeter
- Ammeter
- Fuse
- MCB