NIOS Final Exam Focus

Lesson 15: Electric Charge and Electric Field

Use this sheet for last-minute revision. Focus on laws, definitions, directions of field/force, and standard Gauss law results.

1. Core Facts to Memorize

There are only two kinds of charge: positive and negative.
Like charges repel, unlike charges attract.
Charge is conserved: it is neither created nor destroyed, only transferred.
Charge is quantized: Q = ne, where n is an integer and e = 1.6 × 10^-19 C.
Electron has charge -e, proton has +e, neutron has zero charge.
SI unit of charge is coulomb (C).

2. Coulomb's Law

Applies to point charges at rest.
Force is along the line joining the two charges.
Force is proportional to q₁q₂ and inversely proportional to r².
In vacuum, k = 1/4πε₀ = 9 × 10⁹ N m² C^-2.
In a medium, force decreases by dielectric constant: F_vac/F_medium = ε_r.

F = (1/4πε₀) (q₁q₂/r²)

3. Vector Form and Superposition

Coulomb force is a vector quantity.
For many charges, net force is the vector sum of individual forces.
This is called the principle of superposition.
In numerical problems, always resolve forces or fields carefully by direction.

F₁₂ = (1/4πε₀) (q₁q₂/r²) r̂

4. Electric Field

Electric field at a point is force per unit positive test charge.
Direction of electric field is the direction of force on a positive test charge.
Field due to a positive charge is outward; due to a negative charge is inward.
SI unit: N C^-1.
Force on charge q in field E is F = qE.

E = F/q₀ and E = (1/4πε₀) (q/r²)

5. Electric Dipole

A dipole has two equal and opposite charges separated by a small distance.
Dipole moment direction is from negative to positive charge.
Magnitude of dipole moment: p = q(2l).
At axial position, field is along dipole axis.
At equatorial position, field is opposite to the dipole moment direction.

E_axial = (1/4πε₀) (2p/r³), E_equatorial = (1/4πε₀) (p/r³)

6. Electric Field Lines

Field lines start from positive charges and end on negative charges.
Tangent to a field line gives field direction.
Closer field lines mean stronger electric field.
Two electric field lines never cross.
For a dipole, lines go from positive charge to negative charge.

7. Electric Flux and Gauss's Law

Electric flux measures total electric field passing through a surface.
Gauss's law is important for deriving fields of symmetric charge distributions.
Use Gaussian surfaces only where symmetry is high.
If net enclosed charge is zero, net flux is zero. This does not always mean field is zero everywhere.

Φ_E = E · A and Φ_E = q_enclosed/ε₀

8. Standard Results from Gauss's Law

Point charge: field decreases as 1/r².
Infinite line charge: field decreases as 1/r.
Uniform spherical shell: outside behaves like point charge at centre.
Inside a charged spherical shell: electric field is zero.
Infinite plane sheet: electric field is constant and independent of distance.

Point charge: E = (1/4πε₀)(q/r²)
Line charge: E = σ_l/(2πε₀r)
Plane sheet: E = σ/(2ε₀)

9. NIOS Exam Traps

Do not confuse force with field. Force depends on test charge; field does not.
Inside a conducting spherical shell, field is zero.
For dipole field, axial and equatorial formulas are different in both magnitude and direction.
Flux zero does not imply zero electric field at each point.
Always mention direction in force and field numericals.

10. Van de Graaff Generator

It is an electrostatic generator used to produce very high potential.
Charge is carried by a moving insulating belt.
Sharp combs help transfer charge by corona discharge.
Used for accelerating charged particles and studying nuclear reactions.

11. What to Practice Before Exam

Numericals on Coulomb's law and sharing of charge.
Direction-based electric field questions on axes and triangles.
Dipole field on axial and equatorial positions.
Gauss law derivations for point charge, line charge, spherical shell, plane sheet.
Short notes on electric field lines and Van de Graaff generator.

Best scoring approach: memorize formulas with direction, unit, and where each formula is valid.