Board: West Bengal Council of Higher Secondary Education (WBCHSE) | Class: XII | Subject: Physics (PHYS) | Semester: III | Academic session: 2026–27
Electrostatics is the branch of physics that studies electric charges at rest and the electric effects they produce. It helps explain familiar phenomena such as a comb attracting small pieces of paper, the discharge produced by touching a metal object after walking on a carpet, and the operation of capacitors in electronic circuits. For WBCHSE Class XII students, the topic connects mathematical reasoning with important physical principles.
The WBCHSE Physics syllabus for Class XII Semester III includes electric charges and fields, electric dipoles, electric flux, Gauss’s theorem, electrostatic potential and capacitance. The Council’s published syllabus table assigns this unit 18 contact hours and 8 marks within the 35-mark Semester III theory structure. This is syllabus information, not a guarantee about the exact questions in an examination.
1. Electric Charge and Its Properties
Table of Contents
Electric charge is a basic property of matter. There are two kinds of charge: positive and negative. Like charges repel each other, while unlike charges attract each other. The SI unit of charge is the coulomb (C).
- Additivity: The total charge of a system is the algebraic sum of the individual charges.
- Conservation: Charge is not created or destroyed in an isolated system; it is transferred from one body to another.
- Quantisation: Charge on a body is expressed as q = ne, where n is an integer and e = 1.6 × 10−19 C.
Materials that allow charges to move relatively easily are called conductors. Metals are common examples. Materials in which charges do not move freely are called insulators; dry glass and rubber are examples.
2. Coulomb’s Law: Force Between Two Point Charges
Coulomb’s law states that the electrostatic force between two stationary point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Formula: F = (1 / 4πε0) × |q1q2| / r2 = k|q1q2| / r2, where k ≈ 9 × 109 N m2 C−2 in vacuum, and r is the separation between the charges.
The force acts along the line joining the charges. It is repulsive for like charges and attractive for unlike charges. In a material medium, the force also depends on the medium’s permittivity.
Worked example 1: Calculating electrostatic force
Two positive charges of 2 μC and 3 μC are separated by 0.30 m in air. Find the magnitude of the force between them.
Step 1: Convert the charges into coulombs: q1 = 2 × 10−6 C and q2 = 3 × 10−6 C.
Step 2: Apply Coulomb’s law: F = (9 × 109 × 2 × 10−6 × 3 × 10−6) / (0.30)2.
Step 3: F = 0.054 / 0.09 = 0.60 N. Since both charges are positive, the force is repulsive.
3. Principle of Superposition and Electric Field
When several charges act on a test charge, the net electrostatic force is the vector sum of the forces due to the individual charges. This is the principle of superposition. Remember that forces in different directions must be added as vectors, not simply as ordinary numbers.
The electric field at a point is the force experienced per unit positive test charge placed at that point: E = F/q0. Its SI unit is N/C, which is also equivalent to V/m. The field due to a point charge q at distance r is E = k|q|/r2. The direction is away from a positive source charge and towards a negative source charge.
Electric field lines are a visual way to represent the field. They start from positive charges and end on negative charges, or extend to infinity. Two electric field lines never cross, because the electric field at a point cannot have two different directions.
4. Electric Dipole, Torque and Electric Flux
An electric dipole consists of two equal and opposite charges separated by a small distance. If the separation is 2a and the magnitude of each charge is q, its dipole moment is p = q × 2a. The dipole moment points from the negative charge to the positive charge.
When a dipole is placed in a uniform electric field E, it experiences a torque τ = pE sin θ, where θ is the angle between the dipole moment and the field. The torque tends to align the dipole with the field. For points far from a short dipole, the axial field is approximately 2kp/r3 and the equatorial field has magnitude kp/r3, directed opposite to the dipole moment.
Electric flux measures how much electric field passes through a surface. For a uniform field through a flat surface, Φ = EA cos θ, where θ is the angle between the field and the normal to the surface. The SI unit is N m2/C.
5. Gauss’s Law and Its Applications
Gauss’s law states that the total electric flux through a closed surface equals the net charge enclosed divided by the permittivity of free space:
∮ E · dA = Qenclosed / ε0
It is especially useful when the charge distribution has high symmetry. Standard results included in the syllabus are:
- Infinitely long straight uniformly charged wire: E = λ / (2πε0r), where λ is charge per unit length.
- Infinite uniformly charged plane sheet: E = σ / (2ε0), where σ is charge per unit area.
- Thin uniformly charged spherical shell: Outside, E = kQ/r2; inside the shell, E = 0.
For a numerical or derivation question, first identify the symmetry, then choose a suitable Gaussian surface. Do not apply a memorised result unless the charge distribution and assumptions match the question.
6. Electric Potential and Capacitance
Electric potential at a point is the work done per unit positive test charge in bringing it from infinity to that point, without changing its kinetic energy. For a point charge, V = kq/r. Potential is a scalar quantity, so potentials due to several point charges are added algebraically with their signs.
An equipotential surface has the same potential at every point. Moving a charge along an ideal equipotential surface requires no work. The electric field is perpendicular to an equipotential surface, and in one-dimensional form E = −dV/dr.
A capacitor stores electric charge and electrical energy. Its capacitance is C = Q/V, measured in farads (F). For a parallel-plate capacitor in vacuum, C = ε0A/d, where A is the area of each plate and d is the separation. A dielectric inserted between the plates increases the capacitance by its dielectric constant K in the ideal fully filled arrangement.
- Capacitors in parallel: Ceq = C1 + C2 + …
- Capacitors in series: 1/Ceq = 1/C1 + 1/C2 + …
- Energy stored: U = ½CV2 = ½QV = Q2/(2C).
Worked example 2: Energy stored in a capacitor
A 4 μF capacitor is connected to a 100 V supply. Find the energy stored.
U = ½CV2 = ½ × (4 × 10−6) × (100)2 = 0.02 J.
7. Practice Questions with Answers
- Q1. What is the SI unit of electric field? Answer: N/C or V/m.
- Q2. Two charges are separated by distance r. If the distance is doubled, how does the Coulomb force change? Answer: It becomes one-fourth, because F is proportional to 1/r2.
- Q3. What is the electric field inside an ideal thin uniformly charged spherical shell? Answer: Zero.
- Q4. Two capacitors of 3 μF and 6 μF are connected in series. Find their equivalent capacitance. Answer: 1/C = 1/3 + 1/6 = 1/2, so C = 2 μF.
8. Common Mistakes to Avoid
- Convert μC, nC and cm into SI units before substituting values.
- Keep track of direction when adding electric forces or fields; they are vectors.
- In the flux formula, measure θ from the surface normal, not from the surface itself.
- Do not confuse electric potential (a scalar) with electric field (a vector).
- Use the correct series or parallel rule for capacitors; the rules are opposite to those for resistors.
- In Gauss’s law problems, identify the enclosed charge and use symmetry carefully.
How to Revise Electrostatics Effectively
Prepare a one-page formula sheet, but do not memorise equations without understanding the quantities and their units. Practise drawing field lines and Gaussian surfaces. Solve numerical problems first without looking at the solution, then check each step. Finally, revise the definitions and assumptions behind Coulomb’s law, Gauss’s law, electric potential and capacitance.
Remember: this guide follows the WBCHSE Class XII Physics Semester III syllabus. Students should compare their preparation with the latest instructions and any revised syllabus or question-pattern notice issued by the Council for their own examination session.
Official Source
WBCHSE – Physics syllabus for Classes XI and XII (official PDF)
