Lecture on Electric Charges and Fields

Introduction

• Objective: Complete Electric Charges and Fields in one shot.
• Four parts of content:
  • Charges and Coulomb's Law (30 questions)
  • Field and Applications (25 questions)
  • Dipole and Flux (25 questions)
  • Gauss's Law and Applications (30 questions)
• Format: Lecture and problem-solving with fixed breaks.
• Marks distributed based on +4 for correct answers, -1 for wrong answers.
• Challenges are converted to objectives for NEET, AIIMS, CBSE, other exams.
• Conversion of subjective questions to objective for better engagement.

Key Concepts and Definitions

Charges

• Definition: Intrinsic property of matter that causes it to attract or repel other matter.
• Like charges: Repel.
• Unlike charges: Attract.
• Neutral body: Has no net charge (equal positive and negative charges).
• Quantization of charge: Smallest charge is that of an electron, e = 1.6 * 10^(-19) C. Only multiples of e are possible.
• Conservation of charge: Charge can neither be created nor destroyed.
• Associates with mass: Gains/loses mass when gaining/losing electrons.
• Invariant: Does not change with speed.
• Unit of charge: Coulomb (C), also expressed in esu (electrostatic unit) and emu (electromagnetic unit).

Coulomb's Law

• Formula: F = k * (|q1 * q2| / r^2)
  • k = 9 * 10^9 N m^2 C^-2
  • ε0 (permittivity of free space) = 8.85 * 10^(-12) C^2 N-1m-2
• Vector form: Includes direction with unit vector r^_.
• Superposition Principle: Net force is the vector sum of all individual forces.

Electric Field

• Definition: Region around a charge where its influence is felt by other charges.
• Formula: E = F / q
• Units: N/C (also V/m)
• Properties:
  • Field lines never intersect; they emerge from positive and terminate on negative charges.
  • Perpendicular to the surface of conductors.

Dipole

• Definition: System of two equal and opposite charges separated by a distance.
• Dipole Moment (p): p = q * d
  • From negative to positive charge.
  • Units: C * m
• Field due to Dipole:
  • Along axis: E = 2kp/r^3
  • Perpendicular: E = kp/r^3
  • General Position: Use components.
• Behavior in External Field: Aligns with the field causing torque τ = pE sinθ

Gauss's Law

• Definition: Net flux through any closed surface is proportional to the enclosed charge.
• Formula: Φ = q_inside / ε0
• Implications:
  • Independent of shape and size of the surface.
  • Depends only on the enclosed charge.
  • Can be used to find the field of symmetric charge distributions.

Flux (Φ)

• Definition: Number of electric field lines passing through a given area.
• Formula: Φ = E . A (dot product of electric field and area vector)
• Units: Nm^2/C
• Surface orientations
  • Incoming flux: Negative
  • Outgoing flux: Positive

Applications of Gauss’s Law

Spherical Shell

• Inside (r < R): E = 0
• Outside (r > R): E = kQ/r^2

Solid Sphere

• Inside (r < R): E = (1 / 4πε₀) * (Qr / R³)
• Surface (r = R): E = (1 / 4πε₀) * (Q / R²)
• Outside (r > R): E = (1 / 4πε₀) * (Q / r²)

Infinite Line of Charge

• Field: E = (λ / 2πε₀r)

Plane Sheet of Charge

• Field: E = (σ / 2ε₀)
• Note: Field does not depend on distance from sheet.

Numerical Examples & Practice Problems

• Objective: Solve approximately 95 problems to ensure understanding of the entire chapter.
• Important topics: Include calculations for potential, force, field strengths, and applications of Gauss's Law.

Revision Notes and Mind Map

• Summary: Focused notes on definitions, formulas, units, and properties to aid quick revision.
• Key Topics: Charges, Coulomb’s Law, Electric Field, Dipole, Gauss’s Law, Flux.

Homework

• Complete all questions and derivations discussed in the session.

Conclusion

• Final Emphasis: Endurance and persistence are key. The entire session has been structured to maximize efficiency and understanding, ensuring students are well-prepared for exams.