Electrostatics: The Physics of Static Charge

Hey there! Welcome to the electrifying world of Electrostatics. Don't worry, it's not as scary as it sounds! This chapter is all about the physics of stationary electric charges. Think about the little zap you get from a doorknob, your hair standing on end after taking off a woolly hat, or even a massive lightning strike. That's all electrostatics in action!

In these notes, we'll break down everything you need to know, from the fundamental rules of charge to electric fields, potential, and real-world applications. Let's get started!


1. The Building Blocks: Electric Charge & Charging Methods

Everything starts with charge. It is a fundamental property of matter, just like mass.

a. Two Kinds of Charge: Positive & Negative

In nature, we find two types of electric charge: positive (+) and negative (-).

  • Protons, found in the nucleus of an atom, have a positive charge.
  • Electrons, which orbit the nucleus, have a negative charge.
  • Neutrons, also in the nucleus, are neutral (they have no charge).

An object is electrically neutral when it has an equal number of protons and electrons. Their charges cancel each other out.

b. The Fundamental Rule: Attraction and Repulsion

Opposites Attract, Likes Repel.

  • Two positive charges push each other away (repel).
  • Two negative charges push each other away (repel).
  • A positive charge and a negative charge pull towards each other (attract).

Analogy: Think of it like magnets. Two 'north' poles push each other away, but a 'north' and a 'south' pole snap together!

c. Methods of Charging

In all charging processes, only lightweight, mobile electrons move. Protons remain tightly bound within atomic nuclei.

  • Charging by Friction: Rubbing two different insulating materials causes electrons to transfer from one to the other. The material gaining electrons becomes negatively charged; the one losing electrons becomes positively charged.
  • Charging by Conduction (Contact): When a charged conductor touches an uncharged conductor, electrons flow between them, giving the neutral conductor the same type of charge.
  • Charging by Electrostatic Induction: A charged rod brought near a neutral conductor induces opposite charges on the near side and like charges on the far side. Touching the conductor with a finger (earthing / grounding) allows electrons to enter or leave. Removing the earthing connection before removing the charged rod leaves the conductor with a net charge opposite to that of the rod.

Note on Conductors: On an isolated charged conductor, excess charges repel each other and distribute themselves entirely on the outer surface, concentrating most densely at sharp points.


2. Coulomb's Law: Calculating the Electrostatic Force

Coulomb's Law gives the magnitude of the electrostatic force (\(F\)) between two point charges separated by a distance \(r\).

\( F = \frac{Q_1 Q_2}{4\pi\varepsilon_0 r^2} \)

  • \(F\) is the electrostatic force in newtons (N).
  • \(Q_1\) and \(Q_2\) are the point charges in coulombs (C).
  • \(r\) is the separation distance between the charges in metres (m).
  • \(\varepsilon_0\) is the permittivity of free space (\(\approx 8.85 \times 10^{-12}\text{ C}^2\text{N}^{-1}\text{m}^{-2}\)). The constant \(\frac{1}{4\pi\varepsilon_0} \approx 9.0 \times 10^9\text{ N m}^2\text{C}^{-2}\).

Coulomb's Law obeys an inverse square law: doubling the distance reduces the force by a factor of 4.

Example Calculation

Two charges, \(Q_1 = +2 \times 10^{-6}\text{ C}\) and \(Q_2 = +3 \times 10^{-6}\text{ C}\), are separated by \(0.05\text{ m}\). Find the force between them:

\( F = (9 \times 10^9) \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.05)^2} = (9 \times 10^9) \frac{6 \times 10^{-12}}{0.0025} = 21.6\text{ N} \)

Because both charges are positive, the force is repulsive.


3. Electric Field Strength (\(E\))

An electric field is a region of space where an electric charge experiences an electrostatic force.

a. Field Lines

  • Field lines point in the direction of the force on a positive test charge (away from \(+\), towards \(-\)).
  • The density of field lines represents field strength: closer lines mean a stronger field.
  • Field lines never intersect.

b. Key Formulae for Field Strength

1. General Definition:

\( E = \frac{F}{q} \) (unit: \(\text{N C}^{-1}\) or \(\text{V m}^{-1}\))

2. Electric Field of a Point Charge:

\( E = \frac{Q}{4\pi\varepsilon_0 r^2} \)

3. Uniform Electric Field (Between Parallel Plates):

\( E = \frac{V}{d} \), where \(V\) is the potential difference and \(d\) is the plate separation.


4. Electric Potential (\(V\)) and Potential Energy (\(U\))

Electric potential describes the electrical energy landscape around charges.

  • Electric Potential (\(V\)): The work done per unit positive charge in bringing a small positive test charge from infinity to that point. It is a scalar quantity measured in volts (\(\text{V}\) or \(\text{J C}^{-1}\)).
    For a point charge \(Q\): \( V = \frac{Q}{4\pi\varepsilon_0 r} \)
  • Potential Difference (\(\Delta V\)) and Work Done: The work done \(W\) in moving a charge \(q\) across a potential difference \(\Delta V\) is given by:
    \( W = q\Delta V \)
  • Electric Potential Energy (\(U\)): The energy stored in a system of two point charges \(Q\) and \(q\) separated by distance \(r\):
    \( U = \frac{qQ}{4\pi\varepsilon_0 r} \)

5. Applications and Safety Hazards

  • Electrostatic Precipitator: Highly charged grid wires ionise passing air molecules. Smoke and dust particles pick up negative charge and are attracted to grounded collecting plates, purifying exhaust gases from factories.
  • Lightning Conductors (Action of Points): Sharp metallic points create very high electric fields that ionise air, quietly discharging charged thunderclouds or providing a safe, low-resistance path to the ground if struck.
  • Refuelling Hazards: Friction between flowing fuel and fuel pipes can build up massive static charges. A sudden spark can ignite fuel vapours. To prevent this, aircraft and fuel tankers must be connected with earthing cables before fuel is pumped.
  • Photocopiers: Use electrostatic charge patterns on a photoconductive drum to attract toner particles before transferring them onto paper.