Physics: Electrostatics

This chapter introduces the basic concepts of electrostatics, including electric charges, electric fields, electric potential, Coulomb’s law, and capacitors. These topics are important for students preparing for academic examinations and related departmental assessments.

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1. Production of Electric Charges and Induction

The study of electric charges at rest is known as electrostatics. Electric charge is a fundamental property of matter that causes objects to experience forces of attraction or repulsion.

• Types of Charges:
  Electric charges are classified as positive or negative. Like charges repel each other, while unlike charges attract each other.
• Electrostatic Induction:
  When an uncharged insulated conductor is brought near a charged body, its charges redistribute. One side becomes relatively positive and the other side becomes relatively negative. This process is called electrostatic induction.

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2. The Gold Leaf Electroscope

A gold leaf electroscope is an instrument used to detect the presence of electric charge.

• Structure:
  It consists of a vertical metal rod with a metal disc at the top. The rod is connected to two thin gold leaves inside a protective case.
• Uses:
  An electroscope can detect whether an object is charged. When compared with a charge of known type, it can also help determine whether the unknown charge is positive or negative. It can also help distinguish between conductors and insulators.

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3. Coulomb’s Law of Electrostatic Force

Coulomb’s law describes the electrostatic force between two stationary point charges.

• Statement:
  The electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Formula:
  F = k × q₁q₂ / r²
• Electrostatic Constant:
  In air or vacuum, k is approximately 9 × 10⁹ N·m²·C⁻².

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4. Electric Field and Electrostatic Potential

• Electric Field:
  The region around a charged object in which another charge experiences an electrostatic force.
• Electric Field Intensity:
  Electric field intensity is the force acting on a unit positive test charge.

  Formula: E = F / q₀

  SI unit: newton per coulomb, written as N/C.

• Electric Potential:
  Electric potential at a point is the work done per unit positive charge in bringing the charge from infinity to that point.

  Formula: V = W / q

  SI unit: volt, written as V.

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5. Capacitors and Capacitance

A capacitor is an electronic component that stores electrical energy in an electric field. It usually consists of two conducting plates separated by an insulating material called a dielectric.

• Capacitance:
  Capacitance is the ability of a capacitor to store electric charge.

  Formula: C = Q / V

• Unit of Capacitance:
  The SI unit of capacitance is the farad, written as F. A capacitance of one farad means that one coulomb of charge produces a potential difference of one volt.
• Types of Capacitors:
  Common types include paper capacitors, mica capacitors, variable capacitors, and electrolytic capacitors.

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6. Combinations of Capacitors

Capacitors can be connected in parallel or in series.

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7. Applications and Hazards of Static Electricity

• Practical Applications:
  Static electricity is used in electrostatic air cleaners to remove dust and pollen. It is also used in electrostatic powder coating in some industrial applications.
• Natural Hazards:
  The accumulation of electric charges in storm clouds can produce lightning. Static electricity can also create a fire risk near flammable materials such as petrol vapour.

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8. Calculation-Based Examples

Example 1: Applying Coulomb’s Law

Question:
Two bodies have charges of 500 μC and 100 μC. Find the electrostatic force between them if their separation is 0.5 m in air.

Step-by-Step Solution:

• Distance, r = 0.5 m.
• q₁ = 500 μC = 500 × 10⁻⁶ C.
• q₂ = 100 μC = 100 × 10⁻⁶ C.
• Formula: F = k × q₁q₂ / r².
• Calculation:

  F = [9 × 10⁹ × (500 × 10⁻⁶) × (100 × 10⁻⁶)] / (0.5)²

  F = 1800 N.

• Result:
  Because the charges are opposite, the force is attractive and its magnitude is 1800 N.

Example 2: Capacitors in Parallel

Question:
Three capacitors with capacitances of 3.0 μF, 4.0 μF, and 5.0 μF are connected in parallel across a 6 V battery. Find the total equivalent capacitance.

Step-by-Step Solution:

• Formula:
  C_eq = C₁ + C₂ + C₃
• Calculation:
  C_eq = 3.0 μF + 4.0 μF + 5.0 μF = 12 μF.
• Result:
  The total equivalent capacitance is 12 μF.

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Essential Conceptual Review Questions

Q1: What is electrostatic induction?

Answer:
Electrostatic induction is the redistribution of charge in an insulated conductor caused by the presence of a nearby charged object, without direct physical contact.

Q2: Why are lightning conductors installed on tall buildings?

Answer:
A lightning conductor provides a safe, low-resistance path for electric charge to travel from the highest point of a building into the ground. This helps reduce the risk of damage caused by lightning.