Electrostatics Complete Revision Notes: Electric Charge, Field, Flux and Gauss's Law

Electrostatics is an important topic in Class 12 Physics, with several formulas, concepts and standard results that can be challenging to remember and apply correctly. From Coulomb’s law and electric fields to electric flux and Gauss’s law, understanding the fundamentals is key to solving numerical problems with confidence.

These Electrostatics revision notes bring together the essential formulas, key concepts, important applications and practice questions to help you revise efficiently. Whether you’re preparing for school exams or competitive exams, PW’s revision resources can help you strengthen your understanding, clear up common confusions and approach Electrostatics questions with greater confidence.

What is Electric Charge and What are its Properties?

Electric charge is a basic property of matter that lets a body create an electric or magnetic field and interact with other charged particles. Matter has two basic properties, mass and charge, and charge can be positive or negative. Ordinary bodies become charged by electron transfer. Loss of electrons makes a body positive, gain of electrons makes it negative, and a neutral body has equal positive and negative charge.

The SI unit of charge is the coulomb (C), where 1 C = 1 A x 1 s. Its dimensional formula is [Q] = [AT]. The CGS unit is the statcoulomb (ESU), where 1 C = 3 x 10^9 statcoulomb.

Charge cannot exist without matter, although matter can exist without net charge.

What Are the Methods of Charging?

There are three methods of charging: contact, friction and induction.

• Charging by contact: A charged conductor is connected to a neutral conductor, and charge flows until both reach the same potential (V1 = V2). The final charge on each body depends on its capacitance. Equal capacitance may give equal charges, but different capacitances generally give unequal charges. Both bodies get the same type of charge.

• Charging by friction: Rubbing transfers electrons from one body to the other. The body that loses electrons becomes positive, and the body that gains them becomes negative. At least one body should be non-conducting so that the charge stays separated. The signs depend on relative electronegativities.

• Charging by induction: A charged body is brought near a neutral conductor without touching it. The charges redistribute, the conductor is earthed, and like charge flows to Earth. The earth connection is removed first, then the inducing body. The conductor is left with charge opposite to that of the inducing body.

What Is Coulomb's Law?

For two point charges q1 and q2 separated by distance r, the force between them is:

F = k |q1 q2| / r^2

Here, k = 9 x 10^9 N m^2/C^2 = 1/(4π ε0). This is an inverse-square law, and the force acts along the line joining the charges. Like charges repel and unlike charges attract.

In vector form, F21 = k q1 q2 / r21^2 x (unit vector r21), and F21 = -F12. The scalar form gives only the magnitude, while the vector form gives magnitude and direction. A third charge does not change the force between a given pair, but the net force on any charge is the vector sum of all individual forces.

Coulomb's law applies directly to point charges and uniformly charged spheres. For irregular extended bodies, divide the body into small charge elements and integrate.\

Characteristics of Electrostatic Force

Coulomb’s law holds over a wide range from atomic distances (10⁻¹⁵ m) to many kilometres.

(i) Action Reaction Pair (III Law).

(ii) Defined for point charges (Dimension of charge body is relatively small as compared to separation between bodies).

(iii) Acts along line joining the two charges.

(iv) Force between any pair of charge is independent of any third charge present.

(v) Follows inverse square law.

(vi) Long range force

How Does Coulomb's Law Change in a Medium?

In a medium of permittivity ε, the force is:

F = (1 / 4π ε) x q1 q2 / r^2

The relative permittivity, or dielectric constant, is K = ε / ε0. Therefore:

F (medium) = F (vacuum) / K

Polarisation of the medium separates positive and negative charges, which changes the net force. For the same force in a medium and in vacuum, the equivalent vacuum distance is:

r = d √K

What is Electric Field and Electric Field Intensity?

Electrostatic force is a non-contact, or field, force. The region around a charge where another charge feels a force is called the electric field. Electric field intensity is the force per unit test charge:

E = F / q0

The test charge must be very small so that it does not disturb the original charge distribution. The force on a charge q placed in a field E is F = qE. The electric field is a vector, and its SI units are N/C and V/m.

• A positive charge feels a force along E.

• A negative charge feels a force opposite to E.

• For many charges, E (net) = E1 + E2 + ... as a vector sum.

For a point charge Q, E = k|Q| / r^2. The field points radially outward for a positive charge and radially inward for a negative charge.

How Do You Find the Electric Field of Continuous Charge Distributions?

For an extended body, divide the charge into small elements and integrate. The table gives the standard results, and the notes after it explain how each one is built.

• Charged rod: For a uniformly charged rod, λ = Q/L and dq = λ dx. The small field is dE = k dq / x^2, and the total field is the integral of dE. For a symmetric rod, the parallel components cancel, and only the perpendicular component remains.

• Charged arc: The field acts along the angle bisector. It points away from a positive arc and towards a negative arc.

• Charged ring: Axial components add, while transverse components cancel.

• Charged disc: A disc is treated as a set of concentric rings. For an infinite sheet, the field is constant and does not depend on the distance from the sheet.

• Infinite wire: The field is perpendicular to the wire and varies as 1/r.

What are Electric Field Lines and their Properties?

Electric field lines show the direction of the electric field. The points here explain how to read and draw them correctly.

• They start from positive charges and end on negative charges or at infinity.

• The tangent at any point gives the field direction.

• They never cross each other.

• Closer lines mean a stronger field.

• The number of lines is proportional to the charge.

• They do not form closed loops because electrostatic fields are conservative.

A uniform field has straight, parallel, equally spaced lines. A non-uniform field has changing direction, spacing or both.

What is Electric Flux and the Area Vector?

An area vector is perpendicular to a surface, and its size equals the area. For a closed surface, it always points outward. Electric flux is:

Φ = E . A = EA cos θ

For a general surface, Φ is the integral of E . dA. If the field is normal to the surface (θ = 0°), Φ = EA. If the field is tangential (θ = 90°), Φ = 0. For a closed surface in a uniform field, the entering and leaving flux cancel, so the net flux is zero.

What Is Gauss's Law and Where Is It Used?

Gauss's law states that the integral of E . dA over a closed surface equals q (enclosed) / ε0. The net flux through a closed surface depends only on the enclosed charge. Outside charges may change the field at the surface, but they add zero net flux. A closed surface chosen using charge symmetry is called a Gaussian surface.

The table lists the important results from Gauss's law.

• Charge near a cube: For a charge q at the centre of a cube, the flux through each face is q / 6ε0. For a charge at a vertex, an edge centre or a face centre of the cube, the total flux through the cube is q / 8ε0, q / 4ε0 and q / 2ε0 respectively.

• Spherical cavity: For a cavity inside a uniformly charged sphere, the field is E = ρ d / 3ε0, where d is the vector from the centre of the sphere to the centre of the cavity. The field inside the cavity is uniform.

Electrostatics Important Questions

Solving a mix of conceptual and numerical questions shows how well the formulas have settled in. The questions here cover common exam patterns, with short answers for quick revision.

Question 1

A particle having a charge of 2.0 × 10⁻⁴ C is placed directly below and at a separation of 10 cm from the bob of a simple pendulum at rest. The mass of the bob is 100 g. What charge should the bob be given so that the string becomes loose?

Question 2

Force between two point charges q₁ and q₂ placed in vacuum at ‘r’ cm apart is F. Force between them when placed in a medium having dielectric constant = 5 at ‘r/5’ cm apart will be:

A. F/25
B. 5F
C. F/5
D. 25F

Question 3

Find the magnitude and direction of electric field in a region if a point charge of −5 µC and mass 20 milligrams remains in equilibrium in that region. (g = 10 m/s²)

Question 4

A positively charged particle of mass m and charge q is released from rest in a region of electric field of magnitude E₀ as shown. The region is gravity free. Calculate the speed with which it hits the other end.

Question 5

For the closed hemisphere placed in a uniform electric field as shown in the figure, calculate the flux through its:

(i) Flat surface
(ii) Curved surface

Question 6

A cube is placed inside an electric field, E = 150y² ĵ V/m. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is:

A. 3.8 × 10⁻¹¹ C
B. 8.3 × 10⁻¹¹ C
C. 3.8 × 10⁻¹² C
D. 8.3 × 10⁻¹² C

Question 7

C₁ and C₂ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C₁ and C₂ is:

A. 2 : 5
B. 5 : 2
C. 2 : 3
D. 3 : 2

Key Tips to Revise Electrostatics

Regular practice with direction and sign checks saves many marks in this chapter. The tips here help you avoid the usual mistakes.

• Use repulsion, not attraction, to confirm that a body is charged.

• Treat Coulomb's law as a vector sum when more than two charges are present.

• Divide F (vacuum) by K for the force in a medium, and use r = d√K for the equivalent distance.

• Draw the direction of the field for every charge before adding the fields.

• Use symmetry to cancel components for rods, rings and arcs, and keep only the surviving component.

• Choose a Gaussian surface that matches the charge symmetry.

• Remember that only enclosed charge contributes to net flux in Gauss's law.

• Keep the standard results for spheres, wires and sheets on one formula sheet. 

Regular revision of key formulas, field directions and Gauss’s law applications can help you solve Electrostatics questions more accurately. Practise numerical problems, revise standard results and test your understanding to strengthen your preparation for Class 12 and competitive exams.

 PW's Class 12 online courses and NEET preparation resources offer concept classes and practice sets that can support your Physics revision.

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