Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field. There are two types of charges — positive and negative. Like charges repel each other, while unlike charges attract.
Key Concepts
- Charge quantisation: Every charge in nature is an integer multiple of the elementary charge e = 1.6 × 10-19 C. So Q = ne, where n is an integer.
- Conservation of charge: The total electric charge in an isolated system always remains constant. Charges can neither be created nor destroyed, only transferred.
- Additivity of charge: The total charge of a system is the algebraic sum of all individual charges.
- Coulomb's Law: The force between two point charges q1 and q2 separated by distance r in vacuum is F = k × q1 × q2 / r2, where k = 9 × 109 N m2 C-2. In vector form, the force on q2 due to q1 is along the line joining them.
- Electric Field (E): 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 or V/m.
- Electric field due to a point charge: E = kq / r2, directed radially outward for positive charge and radially inward for negative charge.
- Superposition principle: The total electric field due to multiple charges is the vector sum of the fields due to individual charges.
- Electric field lines: Imaginary lines that show the direction of the electric field. They start from positive charges and end on negative charges; they never intersect.
- Electric Flux (phi): phi = E · A · cos(theta), where theta is the angle between E and the area vector. Unit: N m2 C-1.
- Gauss's Law: The total electric flux through any closed surface (Gaussian surface) equals the net charge enclosed divided by epsilon0. phi = Qenclosed / epsilon0.
- Key Formulas
- Coulomb's force: F = k q1 q2 / r2
- Electric field of point charge: E = kq / r2
- Electric flux: phi = E A cos(theta)
- Gauss's Law: phitotal = Qenc / epsilon0
- Linear charge density: lambda = Q / L; surface: sigma = Q / A; volume: rho = Q / V
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Two point charges +4 µC and -4 µC are placed 0.2 m apart. Find the force between them.
Step 1: q1 = 4 × 10-6 C, q2 = 4 × 10-6 C, r = 0.2 m
Step 2: F = (9 × 109 × 4 × 10-6 × 4 × 10-6) / (0.2)2
Step 3: F = (9 × 109 × 16 × 10-12) / 0.04 = 144 × 10-3 / 0.04 = 3.6 N (attractive)
Find the electric field at 0.3 m from a +2 µC charge.
Step 1: q = 2 × 10-6 C, r = 0.3 m
Step 2: E = kq / r2 = (9 × 109 × 2 × 10-6) / (0.09) = 18000 / 0.09 = 2 × 105 N/C (outward)
A charge of 5 µC is enclosed in a closed surface. Find the total flux through the surface.
phi = Q / epsilon0 = 5 × 10-6 / 8.85 × 10-12 = 5.65 × 105 N m2 C-1
Using Gauss's Law, derive the electric field due to an infinite line charge with linear charge density lambda.
Choose a cylindrical Gaussian surface of radius r and length L coaxial with the wire.
Flux through curved surface = E × 2 pi r L; flux through flat ends = 0.
Charge enclosed = lambda × L.
By Gauss: E × 2 pi r L = lambda L / epsilon0
Therefore E = lambda / (2 pi epsilon0 r)
Two equal positive charges +q are placed at x = +a and x = -a on the x-axis. Find the electric field at the origin.
Field due to +q at x = +a points in the -x direction at origin; field due to +q at x = -a points in the +x direction. Both have equal magnitude kq / a2. They cancel. Net E = 0 at origin.
An electric dipole consists of charges +2 µC and -2 µC separated by 4 cm. Find the dipole moment.
p = q × d = 2 × 10-6 × 0.04 = 8 × 10-8 C·m, directed from -q to +q.
A uniform electric field E = 500 N/C acts along the x-axis. A surface of area 0.2 m2 is tilted at 60° to E. Find the flux.
phi = E A cos(theta) = 500 × 0.2 × cos(60°) = 100 × 0.5 = 50 N m2 C-1
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Common mistakes
- Forgetting that Coulomb's law gives the magnitude of force; direction must be determined separately using the nature of charges.
- Confusing the angle in flux formula — theta is between E and the area vector (normal to the surface), not the surface itself.
- Applying Gauss's law only works easily when the charge distribution has high symmetry (spherical, cylindrical, planar).
Summary
Charge is quantised, conserved, and additive. Coulomb's law and the superposition principle govern electric forces and fields. Gauss's Law provides an elegant way to find E for symmetric charge distributions using the concept of electric flux.