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Electrostatics

Ch. 10Std 11

Easy Overview

Ever get a shock when touching a metal doorknob after walking on a carpet? That is electrostatics - the physics of stationary electric charges. This chapter is about the forces between charged objects, the electric fields they create, the energy stored in those fields, and the potential differences that drive electric currents. You will start from the very basics - what charge is, how it is conserved, and the difference between insulators and conductors. You will then explore Coulomb's law (the electrostatic equivalent of gravity but with both attraction and repulsion), the concept of electric field as a force field around charges, electric potential and potential difference, and capacitors - devices that store charge and energy. Electrostatics is not just about shocks and Van de Graaff generators - it is the foundation of electronics, from tiny capacitors in your phone to lightning protection on buildings.

Electric Charge - Basic Properties

Electric charge is a fundamental property of matter. Two types: positive and negative. Like charges repel, unlike charges attract. Charge is quantized - integer multiples of e = 1.6 x 10^-19 C (charge on one electron). You cannot have 0.5e. The coulomb (C) is the SI unit - a huge amount. One coulomb is the charge of 6.25 x 10^18 electrons. Charge is conserved - in any isolated system, total charge stays constant. Charge cannot be created or destroyed, only transferred. When you rub a glass rod with silk, electrons transfer from glass to silk - glass becomes positive, silk negative. The net charge stays zero. Conductors (metals) allow charge to move freely. Insulators (rubber, plastic) do not.

Coulomb's Law

Coulomb's law: the force between two point charges is proportional to the product of charges and inversely proportional to the square of distance: F = k q_1 q_2 / r^2, where k = 1/(4 pi epsilon_0) = 9 x 10^9 N-m^2/C^2, and epsilon_0 = 8.85 x 10^-12 C^2/N-m^2 is the permittivity of free space. Like charges: F positive (repulsive). Unlike: F negative (attractive). For multiple charges, net force is vector sum (superposition principle). This is trickier than gravity because electrostatic force can be attractive or repulsive. Doubling distance reduces force to one-fourth. The analogy with gravity is strong, but charge can be positive or negative while mass is always positive.

Electric Field

Electric field E at a point is the force that a unit positive charge would experience: E = F/q_0. For a point charge Q: E = kQ/r^2, directed radially away (if Q positive) or toward (if Q negative). Unit: N/C or V/m. Electric field is a vector field. Electric field lines start at positive charges and end at negative charges. Density of lines indicates field strength. Properties: field lines never cross, they are perpendicular to equipotential surfaces, and enter/leave conductors perpendicularly. For a uniform field (between parallel plates), lines are parallel and equally spaced. Inside a conductor in electrostatic equilibrium, E = 0 - that is why you are safe inside a car during lightning (Faraday cage).

Electric Potential and Potential Difference

Electric potential V at a point is work per unit charge to bring a test charge from infinity: V = W/q_0. For a point charge Q: V = kQ/r (taking V = 0 at infinity). Potential is a scalar - much easier than electric field. For multiple charges, just add potentials algebraically. Potential difference delta V = V_2 - V_1 = work per unit charge to move from point 1 to 2. A 12 V battery does 12 J of work per coulomb. The electron volt (eV): energy gained by electron through 1 V: 1 eV = 1.6 x 10^-19 J. Equipotential surfaces: V = constant, always perpendicular to E. Moving charge along equipotential surface does zero work.

Relation Between E and V

The electric field is the negative gradient of potential: E = -dV/dr (1D). In 3D: E = -grad V = -(partial V/partial x i-hat + partial V/partial y j-hat + partial V/partial z k-hat). E points in direction of steepest decrease of potential. Charges naturally move from high to low potential. For uniform field between parallel plates separated by d: V = Ed. If you know the potential function, you can find the field by differentiating. If you know the field, find potential by integrating: V_B - V_A = -integral_A^B E dot dr. Common exam question: given V as function of x, find E.

Capacitors and Capacitance

A capacitor stores charge and electrical energy. Simplest: parallel plate capacitor - two conducting plates separated by insulator. Capacitance C = Q/V. Unit: farad (F). A 1 F capacitor is enormous - most are in microfarads, nanofarads, or picofarads. For parallel plate: C = epsilon_0 A/d. Capacitance depends only on geometry, not on charge or voltage. Larger area ? more capacitance. Smaller separation ? more capacitance. Energy stored: U = 1/2 CV^2 = 1/2 QV = Q^2/(2C). Capacitors are used for: energy storage (camera flash), smoothing voltage fluctuations (power supplies), timing circuits (RC circuits), filtering signals.

Capacitors in Series and Parallel

Series: 1/C_eq = 1/C_1 + 1/C_2 + 1/C_3 + ... Same charge on each, voltage divides. Equivalent capacitance is LESS than smallest individual. Parallel: C_eq = C_1 + C_2 + C_3 + ... Same voltage across each, charge divides. Equivalent capacitance is the SUM. Key tip: series capacitors have SAME Q, parallel capacitors have SAME V. When solving networks: identify series and parallel groups, simplify step by step. The energy stored in combination = sum of energies in each capacitor.

Dielectrics and Polarization

A dielectric is an insulating material between capacitor plates. It increases capacitance by factor K (dielectric constant): C = K C_0, where C_0 is without dielectric. K = epsilon_r (relative permittivity). For parallel plate with dielectric: C = K epsilon_0 A/d = epsilon A/d. How does dielectric increase capacitance? The dielectric's molecules polarize - positive charges shift toward negative plate, negative toward positive. This creates an internal field opposing the applied field, reducing net field. Lower field means you can store more charge for same voltage. Dielectrics also increase breakdown voltage. Different dielectrics: mica (K - 6), paper (K - 3.5), ceramic (K - 100-10000), distilled water (K - 80).

Key Points

  • •Charge quantized (Q = ne, e = 1.6 x 10^-19 C) and conserved. Like repel, unlike attract.
  • •Coulomb's law: F = k q_1 q_2 / r^2, k = 9 x 10^9 N-m^2/C^2 = 1/(4 pi epsilon_0). Superposition applies.
  • •Electric field E = F/q_0. For point charge: E = kQ/r^2 radially. Unit: N/C or V/m.
  • •Field lines start on +Q, end on -Q, never cross, perpendicular to conductors.
  • •Inside conductor in equilibrium, E = 0. Charge on surface. Electrostatic shielding (Faraday cage).
  • •Electric potential V = kQ/r (point charge). Scalar - add algebraically. Unit: volt (J/C).
  • •Potential difference: delta V = -integral E dot dr. E = -dV/dr (gradient).
  • •Equipotential surfaces: V constant, perpendicular to E. Zero work moving charge on them.
  • •Capacitance C = Q/V. Parallel plate: C = epsilon_0 A/d. Energy: U = 1/2 C V^2.
  • •Series: 1/C_eq = sum(1/C_i). Same Q. Parallel: C_eq = sum(C_i). Same V.
  • •Dielectric: C = K C_0 = epsilon A/d. K = epsilon_r. Polarization reduces internal field.
  • •Dielectric strength: max E-field before breakdown. Air: 3 x 10^6 V/m.
  • •Electron volt: 1 eV = 1.6 x 10^-19 J. Energy gained by e- through 1 V.

Practice Questions

  • State Coulomb's law. Three charges q, 4q, and 2q are placed at corners of an equilateral triangle. Find net force on charge at one corner.
  • Define electric field. Find E due to an electric dipole at a point on its axial line.
  • Two point charges +5 microC and -3 microC are 20 cm apart. Find the point on the line joining them where E = 0.
  • Derive the expression for capacitance of a parallel plate capacitor with a dielectric.
  • Three capacitors 2 microF, 3 microF, 6 microF are in series. Find equivalent capacitance.
  • Explain the relation between electric field and potential. If V = 2x^2 + 3y, find E at (1, 2).
  • What is electrostatic shielding? Give an example.
  • A 10 microF capacitor is charged to 100 V. Find the energy stored and the charge on each plate.