Electric Charges and Fields - Lecture Notes

Introduction

• Chapter for 12th standard physics.
• Focus on electric charges and fields.
• Duration of the session: 2.5 hours.
• Aim to cover essential concepts and problems in detail.

Key Concepts

Electric Charge

• Definition of electric charge: Property of matter that causes it to experience a force when placed in an electric field.
• Static Charge: Charges at rest, studied in electrostatics.
• Experiencing Electrostatics: Everyday experiences (e.g., bits of paper attracting when rubbed together).

Methods of Charging

1. Charging by Friction: Rubbing objects together (e.g., glass rod and silk).
2. Charging by Conduction: Transference of charge by direct contact.
3. Charging by Induction: Rearranging charges in an object without direct contact.

Types of Charges

• Two types of charges: Positive and Negative.
• Benjamin Franklin named them.

Charge Interactions

• Like charges repel, unlike charges attract.
• JJ Thomson's Experiment: Discovery of the electron helped define negative charge.
• Charge Quantization: Electric charge exists in discrete amounts, multiples of the elementary charge (1.6 × 10^-19 C).

Properties of Electric Charge

• Additivity of Charges: Total charge is the sum of individual charges.
• Quantization of Charge: Charges are integral multiples of elementary charge.
• Conservation of Charge: Charge cannot be created or destroyed.

Units of Charge

• SI unit of charge: Coulomb (C).
• Charge of an electron: approximately 1.6 × 10^-19 C.

Electric Field

• Definition: A field around a charged object that exerts a force on other charges within the field.

• Direction: Defined as the direction of the force on a positive test charge.

• Formula: Electric field (E) due to a point charge (Q) at distance (r):

  [ E = \frac{kQ}{r^2} ]

• Where k is Coulomb's constant (approximately 9 × 10^9 N m²/C²).

Electric Field due to Multiple Charges

• The net electric field is the vector sum of the electric fields due to individual charges.

Electric Field Lines

• Representation of electric fields.
• Lines originate from positive charges and terminate at negative charges.
• Cannot intersect; at any point, the electric field can have only one direction.

Electric Dipole

• Definition: Consists of two equal and opposite charges, separated by a distance (d).
• Dipole Moment (P): Defined as [ P = q imes d ]
• Direction of dipole moment vector is from negative to positive charge.

Gauss's Law

• Total electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ε0).
• [ \Phi_E = \frac{Q_{enc}}{\epsilon_0} ]_

Applications of Gauss's Law

1. Electric Field due to an Infinite Plane Sheet:
   • Electric field (E) is constant and given by [ E = \frac{\sigma}{2\epsilon_0} ]
   • Where σ is surface charge density.
2. Electric Field due to an Infinite Line of Charge:
   • Electric field (E) at distance r from line charge is [ E = \frac{\lambda}{2\pi r \epsilon_0} ]
   • Where λ is linear charge density.
3. Electric Field due to a Spherical Shell:
   • Inside the shell: Electric field (E) is zero.
   • Outside the shell: behaves as point charge [ E = \frac{Q}{4\pi r^2} ]

Important Formulas

• Electric Field from a Point Charge: [ E = \frac{kQ}{r^2} ]
• Electric Field from a Dipole: [ E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3} ]
• Electric Flux: [ \Phi_E = E \cdot A ]

Conclusion

• Covered key concepts in electric charges and fields, including properties, methods of charging, and applications of Gauss's law.
• Important for students preparing for exams like NEET and JEE.
• Session aimed to encourage participation and understanding of fundamental physics concepts.