Electrostatics
Easy Overview
Ever rubbed a balloon on your hair and watched it stick to the wall? That's static electricity — the same force that causes lightning bolts. This chapter is about charges at rest: why they attract or repel, how to calculate the force between them, and what happens when you bring charges near conductors. It's the foundation of all electricity.
Coulomb's Law — The Force Between Charges
Like charges repel, opposite charges attract. The force between two point charges is F = k q₁q₂ / r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C². ε₀ is the permittivity of free space (8.85 × 10⁻¹²). The force is along the line joining the charges. Coulomb's law looks just like Newton's gravity law — but charges can attract or repel, while gravity only attracts.
Electric Field — The Invisible Influence
An electric field is the region around a charge where it exerts force on other charges. E = F/q₀ (force per unit test charge). For a point charge, E = kQ/r², directed radially outward (positive) or inward (negative). Electric field lines start from positive charges and end on negative charges. They never cross. The denser the lines, the stronger the field. It's like a wind map showing which way a charge would feel a push.
Electric Potential — Voltage for Short
Electric potential V is the work done per unit charge to bring a test charge from infinity to that point. V = kQ/r for a point charge. Potential difference ΔV = W/q — that's what we call voltage. Charges flow from higher potential to lower potential. Equipotential surfaces connect points with the same potential — no work is done moving a charge along them. They're perpendicular to electric field lines.
Capacitors — Storing Charge
A capacitor stores electrical energy. The simplest is two parallel plates: C = ε₀A/d, where A is plate area, d is separation. Capacitance C = Q/V — how much charge it holds per volt. Dielectrics are insulators that increase capacitance when placed between plates (by a factor of κ, the dielectric constant). Energy stored in a capacitor: U = ½CV² = ½QV. Capacitors in parallel add: C_total = C₁ + C₂ + ... In series: 1/C_total = 1/C₁ + 1/C₂ + ...
Gauss's Law — The Big Picture
Gauss's law says the total electric flux through a closed surface equals the charge enclosed divided by ε₀. Φ = ∮ E·dA = q_enclosed / ε₀. It sounds abstract, but it makes calculating fields for symmetrical charge distributions super easy. For example, the field outside a uniformly charged sphere is the same as if all charge were at the center. It's a shortcut — skip messy integrals when you have symmetry.
Key Points
- •Coulomb's law: F = k q₁q₂ / r², k = 9×10⁹ N·m²/C²
- •Electric field E = F/q₀, direction from + to −
- •Potential V = kQ/r, Potential difference = work/charge
- •Capacitance C = Q/V, Parallel plate: C = ε₀A/d
- •Dielectric increases capacitance by factor κ
- •Capacitors in parallel: C_total = C₁ + C₂ + ..., in series: 1/C_total = 1/C₁ + 1/C₂ + ...
- •Gauss's law: Φ = q_enclosed / ε₀
- •Electric field inside a conductor is zero (electrostatic equilibrium)
Practice Questions
- Two charges 5 μC and −3 μC are placed 20 cm apart. Find the force between them.
- Derive an expression for the capacitance of a parallel plate capacitor with a dielectric slab.
- State Gauss's law and use it to find the electric field due to an infinitely long charged wire.
- Three capacitors 2 μF, 3 μF, and 5 μF are connected in series to a 12 V battery. Find total capacitance and charge on each.