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Full Physics Short Notes (Part 1) – Electric Charge to Electrostatic | Class 12 & JEE 2026

 

⭐ Full Physics  Short Notes (Part 1) | Class 12 Physics & JEE 2026

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The chapter Electric Charges and Fields introduces one of the most important concepts in Physics — electric charge and how charges interact with each other using forces, electric fields, lines of force, and Gauss's law.

The chapter Electrostatic Potential and Capacitance explains how charges create potentials, how electric fields relate to potential, and how capacitors store charge. This is one of the most scoring chapters in CBSE Boards, JEE Main, NEET, and other competitive exams.

These notes cover all the essential formulas, graphs, concepts, and definitions that you need for Boards, JEE, NEET, and Olympiads.



✅ SECTION 1 - ELECTRIC CHARGES AND FIELD

πŸ”΅ 1. Electric Charge

Electric charge is a fundamental property of matter responsible for electromagnetic interaction between objects.

✔ Key properties

  • Two types of charges: positive & negative

  • Measured in coulomb (C)

  • Quantized

  • Additive (algebraic sum)

If total charge = q₁ + q₂ + q₃ … then net charge is simple addition.

πŸ”΅ 2. Coulomb’s Law

It gives the force between two static point charges:

\[ F=\frac{1}{4\pi\epsilon_0\epsilon_r}\cdot\frac{q_1 q_2}{r^2} \]

Where:

  • Ξ΅₀ = permittivity of free space

  • Ξ΅α΅£ = dielectric constant of medium

  • r = distance between charges

✔ Direction

  • Repulsive for like charges

  • Attractive for unlike charges

✔ Limitations

  • Applicable only for point charges at rest

πŸ”΅ 3. Principle of Superposition

When multiple charges act on a charge, the net force is the vector sum:

\[ \vec{F}_{\text{net}}=\vec{F}_1+\vec{F}_2+\vec{F}_3+\dots \]

One charge does not disturb the force of another.

πŸ”΅ 4. Electric Field (E)

Electric field at a point:

\[ \vec{E}=\frac{\vec{F}}{q} \]

Unit → N/C or V/m
Direction → direction of force on positive test charge

πŸ”΅ 5. Electric Field Due to a Point Charge

\[ E=\frac{1}{4\pi\epsilon_0}\cdot\frac{q}{r^2} \]

Direction: outward for positive charge, inward for negative.

πŸ”΅ 6. Null Point Between Two Charges

For two charges Q₁ and Q₂:

If Q₁ > Q₂ → null point lies closer to Q₂.

Distance from Q₁:

\[ x=\pm r\sqrt{\frac{Q_1}{Q_2}} \]

  • ‘+’ for like charges (between them)

  • ‘–’ for unlike charges (outside)

πŸ”΅ 7. Equilibrium of Three Charges

For three collinear charges Q₁—q—Q₂:

Conditions :

  • Q₁ and Q₂ must be like charges

  • q must be opposite charge

From equilibrium:

\[ x = \frac{Q_1 - Q_2}{Q_1 + Q_2} \]

πŸ”΅ 8. Electric Dipole

Electric dipole = two equal and opposite charges separated by distance d.

Dipole moment:

\[ \vec{p} = q \vec{d} \]

Torque in a uniform field:

\[ \vec{\tau} = \vec{p} \times \vec{E} \]

πŸ”΅ 9. Electric Field Due to a Dipole

⭐ At any general point:

\[ E = \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^3} \sqrt{1 + 3 \cos^2 \theta} \]

⭐ Axial (End-on) Position:

\[ E_{\mathrm{axial}} = \frac{1}{4 \pi \varepsilon_0} \frac{2p}{r^3} \]

⭐ Equatorial Position:

\[ E_{\mathrm{equatorial}} = \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^3} \] (but opposite direction)

πŸ”΅ 10. Electric Lines of Force

Properties:

  1. Imaginary and represent direction of electric field

  2. Never cross each other

  3. Never form closed loops

  4. Number of lines ∝ magnitude of charge

  5. They start/end normally on conductor surfaces

  6. No lines exist in zero field region

  7. Crowded lines → strong field; spaced → weak field

  8. Tangent at any point gives electric field direction

πŸ”΅ 11. Electric Flux (Ξ¦)

\[ \phi = \int \vec{E} \cdot d\vec{s} \]

Unit: N·m²/C

πŸ”΅ 12. Gauss’s Law

\[ \oint \vec{E} \cdot d\vec{s} = \frac{q_{\mathrm{enclosed}}}{\varepsilon_0} \]

Applies only on closed surfaces.

πŸ”΅ 13. Electric Field for Different Charge Distributions

⭐ A. Point Charge

\[ E = \frac{k q}{r^2} \]

Direction: radial

⭐ B. Infinite Line Charge

\[ E = \frac{\lambda}{2 \pi \varepsilon_0 r} \]

Ξ» = linear charge density

⭐ C. Infinite Non-Conducting Sheet

\[ E = \frac{\sigma}{2 \varepsilon_0} \]

Οƒ = surface charge density

⭐ D. Infinite Conducting Sheet

\[ E = \frac{\sigma}{\varepsilon_0} \]

⭐ E. Uniformly Charged Ring

At a point on axis distance x:

\[ E = \frac{k Q x}{(R^2 + x^2)^{3/2}} \]

Max when x = R/√2

⭐ F. Charged Conducting Sphere

For r ≥ R:

\[ E = \frac{k Q}{r^2} \quad (r \ge R) \]

For r < R:

\[ E = 0 \quad (r < R) \]

Acts like all charge is at center.

⭐ G. Solid Non-Conducting Sphere

For r ≤ R:

\[ E = \frac{k Q r}{R^3} \quad (r \le R) \] (Directly proportional to r)

For r ≥ R:

\[ E = \frac{k Q}{r^2} \quad (r \ge R) \]

⭐ H. Long Charged Cylinder

For r ≥ R:

\[ E = \frac{q}{2 \pi \varepsilon_0 r L} \quad (r \ge R) \]

For r < R:
\[ E = 0 \quad (r < R) \] E = 0

πŸ”΅ 14. Additional Formulas (From PDF)

✔ Electric field near a conductor

\[ E = \frac{\sigma}{\varepsilon_0} \]

✔ Electrostatic pressure

\[ P = \frac{\sigma^2}{2 \varepsilon_0} \]

✔ Energy density of electric field

\[ u = \frac{1}{2} \varepsilon_0 E^2 \]

🟩 Short Revision Notes

  • Charge is quantized & additive

  • Coulomb’s law → inverse square law

  • Superposition → vector addition

  • Dipole moment → \(\vec{p} = q \vec{d}\)

  • Axial field > equatorial field

  • Lines never cross

  • Gauss’ law → flux depends only on enclosed charge

  • Field inside conductor = 0

  • Solid sphere → E ∝ r (inside)

  • Conducting sphere → E = 0 (inside)

  • Electric pressure ∝ Οƒ²

  • Ring field maximum at \(x = \frac{R}{\sqrt{2}}\)


✅ SECTION 2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE 

πŸ”΅ 1. Relation Between Electric Field and Electric Potential

The potential at a point is the work done per unit charge in bringing a test charge from infinity to that point.

The relation between E and V is:

\[ \vec{E} = -\nabla V \]

Or in components:

\[ E_x = -\frac{\partial V}{\partial x}, \quad E_y = -\frac{\partial V}{\partial y}, \quad E_z = -\frac{\partial V}{\partial z} \]

This means the electric field always points in the direction of maximum decrease of potential.

πŸ”΅ 2. Electric Potential Energy of Two Point Charges

For two charges ( q_1 ) and ( q_2 ) separated by distance ( r ):

\[ U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} \]

  • If both charges have same sign → ( U > 0 ) (repulsion)

  • If signs are opposite → ( U < 0 ) (attraction)

πŸ”΅ 3. Electric Potential Due to an Electric Dipole

Dipole moment:

\[ p = qd \]

At a point distance r from center, making angle ΞΈ with dipole axis:

\[ p = qd \]

πŸ”΅ 4. Equipotential Surfaces

Equipotential surfaces = surfaces where potential is same everywhere.

key properties:

  • No work done in moving charge on an equipotential surface

  • Electric field is perpendicular to equipotential surfaces

  • Conductor’s body is an equipotential region

πŸ”΅ 5. Potential Due to Different Charge Distributions

⭐ A. Potential Due to a Point Charge

\[ V = \frac{k q}{r} \]

Graph: Hyperbolic decreasing with r.

⭐ B. Potential Due to a Conducting Sphere

For r ≥ R:

\[ V = \frac{k q}{r} \]

For r < R (inside sphere):

\[ V = \frac{k q}{R} \]

Electric field inside = 0.

⭐ C. Potential Due to a Non-Conducting Solid Sphere

For r ≥ R:

\[ V = \frac{k Q}{r} \]

For r < R:

\[ V = \frac{k Q}{2 R^3} (3 R^2 - r^2) \]

Important:

  • Potential at center = ( \(V_{\mathrm{center}} = \frac{3 k Q}{2 R}\) )

  • Potential at surface = ( \(V_{\mathrm{surface}} = \frac{k Q}{R}\) )

  • Ratio: Vcenter:Vsurface=3:2V_{\mathrm{center}} : V_{\mathrm{surface}} = 3:2

⭐ D. Potential of a Spherical Shell (Conducting / Non-Conducting)

Same as conducting sphere:

  • For ( r < R ) → constant

  • For ( r ≥ R ) → ( \(V = \frac{k Q}{r}\) )

⭐ E. Potential Due to a Charged Ring

At center:

\[ V = \frac{k Q}{R} \]

At distance x on axis:

\[ V = \frac{k Q}{\sqrt{R^2 + x^2}} \]

  • Maximum potential at x = 0

  • Maximum electric field at ( \(x = \pm \frac{R}{\sqrt{2}}\) )

⭐ F. Potential Due to Infinite Line Charge

\[ V_B - V_A = 2 k \lambda \ln \left(\frac{r_B}{r_A}\right) \]

Absolute potential not defined, but potential difference is:

⭐ G. Potential Due to Infinite Non-Conducting Sheet

\[ V_B - V_A = \frac{\sigma}{2 \epsilon_0} (r_B - r_A) \]

Not absolute, only potential difference:

⭐ H. Potential Due to Infinite Conducting Sheet

\[ V_B - V_A = \frac{\sigma}{\epsilon_0} (r_B - r_A) \]

(Note: Twice the non-conducting sheet value.)

πŸ”΅ 6. Capacitance

⭐ A. Definition

Capacitance (C) measures the ability to store charge:

\[ C = \frac{Q}{V} \]

Unit → Farad (F)

⭐ B. Parallel Plate Capacitor

With dielectric:
\[ C = \frac{\epsilon_0 \epsilon_r A}{d} \]

Without dielectric:
\[ C = \frac{\epsilon_0 A}{d} \]

πŸ”΅ 7. Energy Stored in a Capacitor

\[ U = \frac{1}{2} C V^2 \]

Alternative forms:

\[ U = \frac{Q^2}{2 C} = \frac{1}{2} Q V \]

πŸ”΅ 8. Electric Field Between Capacitor Plates

\[ E = \frac{\sigma}{\epsilon_0} \]

Independent of separation for ideal capacitor.

πŸ”΅ 9. Energy Density of Electric Field

\[ u = \frac{1}{2} \epsilon_0 E^2 \]

Represents energy stored per unit volume.

πŸ”΅ 10. Electrostatic Pressure on Conductors

\[ P = \frac{\sigma^2}{2 \epsilon_0} \]

Occurs because charges repel outward on conductor surfaces.

🟩 Short Revision Checklist

  • ( \(\vec{E} = -\nabla V\) )

  • Dipole potential \(\propto \frac{1}{r^2}\)

  • V for conducting sphere is constant inside

  • V at center of non-conducting sphere = \(\frac{3 k Q}{2 R}\)

  • Potential of ring max at \(x = 0\)

  • Capacitor: \(C = \frac{\epsilon_0 A}{d}\)

  • Energy in capacitor = \(\frac{1}{2} C V^2\)

  • Pressure = \(\frac{\sigma^2}{2 \epsilon_0}\)

  • Infinite sheet potentials → only potential difference defined


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