Electrostatics
Easy Overview
Ever gotten a shock after rubbing your feet on a carpet and touching a door handle? That's electrostatics — charges sitting still, waiting to jump. This chapter is about what happens when electric charges aren't moving, how they push and pull each other, and how we store that charge for later use.
Gauss's Law
Gauss's law is a clever way of saying 'the total electric field flowing out of a closed surface depends only on the charge inside.' Imagine blowing soap bubbles around a light bulb — the amount of light passing through the bubble depends only on how bright the bulb is, not on the shape or size of the bubble. Same with electric fields. This law makes it dead simple to calculate fields for symmetrical things like spheres, cylinders, and infinite sheets. No messy integrals needed.
Electric Potential and Potential Energy
Electric potential is like height for charges. A charge at a high potential wants to move to a low potential, just like a ball rolls downhill. The voltage of a battery is the potential difference between its terminals — it tells you how much energy each unit of charge gets as it goes through the battery. Work done to move a charge between two points equals the charge times the potential difference. That's what 'voltage' really means — it's the push that makes charges move.
Capacitors
A capacitor is a charge-storing device — two metal plates separated by a gap. When you connect it to a battery, one plate gets positive and the other negative. They store energy in the electric field between them. Think of it like a water tank — you fill it up (charge it), and later you can release the water (discharge it). Capacitors are everywhere — in camera flashes (quick burst of energy), in power supplies (smoothing out voltage), and in circuits (timing and filtering).
Dielectrics
A dielectric is an insulator you put between capacitor plates. It increases the capacitance significantly. Why? Because the material's molecules polarize — positive and negative ends align opposite to the field. This reduces the effective field inside, allowing more charge to be stored for the same voltage. Think of it as the dielectric 'absorbing' some of the electric field. Different materials have different dielectric constants — higher constant = more charge storage.
Key Points
- •Gauss's law: ∮E·dA = Q/ε₀. The electric flux through a closed surface depends only on enclosed charge.
- •Electric potential V = kQ/r. Potential difference between two points is the work done per unit charge.
- •Capacitance C = Q/V. For parallel plate capacitor, C = ε₀A/d.
- •A capacitor stores energy: U = ½CV².
- •Dielectric increases capacitance by factor K (dielectric constant).
- •Capacitors in series: 1/Ceq = 1/C₁ + 1/C₂ + ... In parallel: Ceq = C₁ + C₂ + ...
Practice Questions
- State Gauss's law. Use it to find the electric field due to an infinitely long charged wire.
- Derive the expression for the capacitance of a parallel plate capacitor with a dielectric between the plates.
- Three capacitors of 2 µF, 3 µF, and 6 µF are connected in series. Find the equivalent capacitance.
- Explain the concept of electric potential. Derive an expression for electric potential due to a point charge.