Electric Field in Electrostatics – Complete Theory, Formula & Applications | Taxtron

Electrostatics – Complete Conceptual Guide for ISC & JEE Physics

Introduction to Electrostatics

Electrostatics is the branch of physics that deals with electric charges at rest and the forces, fields, and potentials associated with them. It forms the foundation of electricity, electromagnetism, electronics, and modern physics, making it one of the most important chapters for ISC Class 12, JEE Main, and JEE Advanced.

Almost every electrical device you see today—from capacitors in circuits to sensors and displays—relies on principles derived from electrostatics.

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Electric Charge-Searching Something else Search

Nature of 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, while unlike charges attract.

Basic Properties of Charge

1. Additivity – Total charge is the algebraic sum of individual charges

2. Conservation of charge – Charge can neither be created nor destroyed

3. Quantization of charge –

   $$q = ne \quad \text{where } e = 1.6 \times 10^{-19}\,\text{C}$$

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Methods of Charging a Body

1. Charging by Friction
   Transfer of electrons due to rubbing (e.g., glass rod and silk)

2. Charging by Conduction
   Direct contact allows charge transfer

3. Charging by Induction
   Charging without contact using a nearby charged body
   → Very important for JEE conceptual questions

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Coulomb’s Law

Coulomb’s law gives the force between two stationary point charges:

$$F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}$$

Key Points

• Force acts along the line joining the charges

• Inverse square law

• Medium dependent

  $$F = \frac{1}{4\pi\varepsilon}\frac{q_1 q_2}{r^2}$$

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Electric Field

The electric field at a point is defined as the force experienced by a unit positive test charge placed at that point.

$$\vec{E} = \frac{\vec{F}}{q}$$

Electric Field Due to Point Charge

$$E = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}$$

Electric Field Lines

• Originate from positive charge

• Terminate on negative charge

• Never intersect

• Density represents strength

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Electric Flux

Electric flux measures the number of electric field lines passing through a surface.

$$\Phi_E = \vec{E} \cdot \vec{A}$$

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Gauss’s Law

One of the most powerful laws in electrostatics:

$$\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0}$$

Applications of Gauss’s Law

• Electric field due to:

  • Infinite line charge

  • Infinite plane sheet

  • Spherical shell (conducting & non-conducting)

JEE Tip: Always identify symmetry before applying Gauss’s law.

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Electric Potential

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

$$V = \frac{W}{q}$$

Potential Due to Point Charge

$$V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}$$

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Relation Between Electric Field and Potential

$$\vec{E} = -\nabla V$$

In one dimension:

$$E = -\frac{dV}{dx}$$

This relation is extremely important for numerical problems and graphs.

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Equipotential Surfaces

• Surfaces having same electric potential

• No work is done in moving a charge along an equipotential surface

• Electric field is always perpendicular to equipotential surfaces

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Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance.

Dipole Moment

$$\vec{p} = q \cdot 2a$$

Electric Field Due to Dipole

• On axial line

• On equatorial line

Torque on a Dipole

$$\tau = pE \sin\theta$$

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Electrostatics of Conductors

Key properties:

• Electric field inside conductor = 0

• Charge resides on surface

• Surface is an equipotential

• Electric field just outside conductor:

  $$E = \frac{\sigma}{\varepsilon_0}$$

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Capacitance

Capacitance is the ability of a conductor to store electric charge.

$$C = \frac{Q}{V}$$

Parallel Plate Capacitor

$$C = \frac{\varepsilon_0 A}{d}$$

With dielectric:

$$C = K\frac{\varepsilon_0 A}{d}$$

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Energy Stored in a Capacitor

$$U = \frac{1}{2}CV^2 = \frac{1}{2}QV = \frac{Q^2}{2C}$$

Energy density:

$$u = \frac{1}{2}\varepsilon_0 E^2$$

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Importance of Electrostatics in Real Life

• Capacitors in electronic circuits

• Photocopiers and laser printers

• Electrostatic precipitators

• Touchscreens and sensors

• Particle accelerators

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Exam Strategy for ISC & JEE

• Master Gauss’s law applications

• Focus on field–potential relationship

• Practice graph-based problems

• Memorize standard results (shells, planes, lines)

• Solve PYQs after concept clarity

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Explore Chemistry Reactions & Mechanisms (Search Tool)

To study chemical reactions, mechanisms, conversions, and theory, use our dedicated search page:

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This tool allows you to search reactions by name, formula, or mechanism, and will expand with more standalone theory pages over time.

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Conclusion

Electrostatics is not just a chapter—it is the gateway to understanding electricity, magnetism, and modern electronics. A strong conceptual grip on this topic ensures success not only in ISC and JEE, but also in higher studies of physics and engineering.

This page is designed as a complete self-study reference, and will be continuously supported with tools, simulations, and linked resources across the site.