Phenomena of Static Electricity

  • Observations:
    • Sparks or crackles when removing synthetic clothes in dry weather.
    • Lightning during thunderstorms.
    • Electric shocks when touching metallic objects after rubbing against surfaces.
  • Cause:
    These are examples of static electricity caused by the accumulation and discharge of charges from insulating surfaces.

Introduction to Electrostatics

  • Static Electricity: Charges that don’t move or change with time.
  • Electrostatics: The study of forces, fields, and potentials caused by static charges.

Electric Charge

  • Historical Insight:
    • Discovered by Thales of Miletus (600 BC), who noticed amber rubbed with wool attracted light objects.
    • “Electricity” comes from the Greek word “elektron” (amber).
  • Key Observations:
    • Like charges repel, and unlike charges attract.
    • Example: A glass rod rubbed with silk and a plastic rod rubbed with fur exhibit attraction and repulsion based on the charge polarity.
  • Polarity of Charge:
    • Glass rod → Positive charge.
    • Silk cloth → Negative charge (Benjamin Franklin’s convention).
    • Charges can neutralize each other when opposite charges come into contact.
  • Gold-leaf Electroscope:
    • A device to detect electric charge.
    • Mechanism: When a charged object touches the knob, charges flow to the gold leaves, causing them to diverge.

Why Materials Acquire Charge

  • Structure of Matter:
    • Matter is made up of atoms, which are neutral but contain charges.
    • Rubbing transfers electrons, causing one object to gain (negative charge) and another to lose electrons (positive charge).
  • Charge Properties:
    • Positive Charge: Loss of electrons.
    • Negative Charge: Gain of electrons.
    • Charges transfer but are neither created nor destroyed, adhering to the law of conservation of charge.

Conductors and Insulators

  • Conductors: Allow free movement of electrons. Examples: Metals, human bodies, and earth.
  • Insulators: Resist electron flow. Examples: Glass, plastic, wood.
  • Practical Insight:
    • Metal charges leak away when held because the human body conducts electricity.
    • A nylon comb can hold charge due to its insulating nature.

Basic Properties of Electric Charge

  1. Additivity of Charge:
    • Charges add algebraically (e.g., +3 C + (-1 C) = +2 C).
  2. Conservation of Charge:
    • Total charge in an isolated system remains constant.
    • Example: Rubbing transfers charge without creating new charges.
  3. Quantisation of Charge:
    • Charge (qqq) is always an integer multiple of the elementary charge (e=1.6×10−19C).
    • At macroscopic levels, charge appears continuous due to its large scale compared to e.

Coulomb’s Law

  • Definition:
    • The force (F) between two point charges q1​ and q1​ separated by distance r in a vacuum: F= k (q1q2/r2)​​ where k= 9×109 Nm2/C2 (electrostatic constant).
  • Insights from Coulomb’s Experiments:
    • Force is directly proportional to the product of charges.
    • Force is inversely proportional to the square of the distance.
    • Charges interact along the line joining them.

Examples for Better Understanding

  1. Electrons Transfer Example:
    • 10910^9109 electrons leave a body per second. To transfer a total charge of 1 C:
      • Time required = 6.25×109 seconds (~200 years).
      • Conclusion: 1 C is a large amount of charge.
  2. Charge in Water:
    • A cup of water (~250 g) contains: Total charge= 1.34×107C (balanced positive and negative charges).

Competitive Question Tips

  1. Conceptual Questions:
    • Explain why like charges repel.
    • Why does a nylon comb get electrified while metal doesn’t?
  2. Numerical Questions:
    • Use p= ne for charge quantisation problems.
    • Apply Coulomb’s law for force between charges.
  3. Practical Insight:
    • Understand the role of conductors and insulators in daily life scenarios.
    • Learn charge conservation with examples like rubbing or electroscope.

Forces Between Multiple Charges

  1. Coulomb’s Law for Two Charges
    • The electric force between two stationary charges is given by Coulomb’s law:
      F= 1/4πε0  p1p2/r2 r
      where q1 and q2​ are the charges, rrr is the distance between them, and r^ is the unit vector in the direction of the force.
  2. Multiple Charges: Superposition Principle
    • When multiple charges are present, the total force on a charge is the vector sum of individual forces exerted by each charge.
    • Superposition Principle: Forces due to individual charges are calculated as if the other charges do not exist. These forces are then added vectorially.
  3. Example: Three Charges (q₁, q₂, q₃)
    • Consider charges q1​, q2​, and q3​.
    • The total force on q₁​ is: F1​=F12​+F13​,
      • where: F12​= 1/4πε0 q1​q2/r2 ​​r^12 and F13​= 1/4πε0 q1​q3/r2 ​​r^13
  4. General Case (n Charges)
    • For nnn charges(q1, q2, …, qn), the force on q1​ is: F1​= ∑n i=2​F1i​, where F1i​ is the force due to charge qi on q1​.
  5. Applications of Superposition
    • Symmetry Simplifications: If charges are symmetrically placed, the resultant force can sometimes be zero.
    • Example: In an equilateral triangle, if charges of the same magnitude are symmetrically placed, the net force on a charge at the centroid is zero due to symmetry.
  6. Key Formulae for Competitive Exams
    • Force due to multiple charges:F1​=1/4πε0​1​i=2∑n q1qi/r2 r1i​.
    • Resultant force using vector addition: Apply the parallelogram or triangle law of vector addition.
  7. Worked-Out Examples
    • Example 1: Charges q,q,−q at vertices of an equilateral triangle of side lll:
      • The force on q at one vertex is calculated using vector addition of forces due to the other two charges.
      • Result: Symmetry often simplifies calculations.
  8. Electric Field Concept
    • Definition: The electric field E at a point is the force experienced by a unit positive test charge placed at that point.
    • Formula:E= F
      ​/q=1 Q/4πε0​ ​r2  r^.
      • Q: Source charge.
      • r: Distance from the source charge.
  9. Electric Field Due to Multiple Charges
    • Use the superposition principle for electric fields: E(r)=i=1∑n 1/4πε0​ q1/r2ip r^ip
  10. Practical Tips for Problem Solving
    • Identify Forces/Fields: Write expressions for forces or fields due to each charge.
    • Use Symmetry: Simplify calculations by identifying symmetrical setups.
    • Vector Addition: Use components or graphical methods for summing vectors.
    • Units and Constants: Ensure proper use of constants like ε0 (permittivity of free space).
  11. Special Considerations
    • Field lines: For positive charges, field lines radiate outwards; for negative charges, they converge inward.
    • Dependence on distance: Both force and field decrease with the square of the distance.

*Further notes are comong soon*