Physics Chapter 1 Electric Charges and Fields Class 12 Notes - FREE PDF

Electric Charges and Fields

1. Electric Charge

• Definition: Charge is a property of matter that produces and experiences electrical and magnetic effects.

• Types of Charge:

  • Positive Charge

  • Negative Charge

• Behavior:

  • Like charges repel each other.

  • Opposite charges attract each other.

• Units:

  • S.I. unit: Coulomb (C)

  • C.G.S. unit: electrostatic unit (e.s.u.)

• Dimensional Formula: [Q] = [AT]

1.1 Point Charge

• Defined as a particle whose spatial size is negligible compared to the distances involved.

1.2 Properties of Charge

• Scalar Quantity: Can be added or subtracted algebraically.

• Transferable: Charge can transfer between bodies in contact.

• Associated with Mass: Charge cannot exist without mass, though mass can exist without charge.

• Conserved: Charge is neither created nor destroyed.

• Invariance of Charge: The value of the elementary charge is independent of velocity.

• Electric and Magnetic Fields: A stationary charged particle produces an electric field, an unaccelerated one produces both electric and magnetic fields, and an accelerated particle radiates energy as electromagnetic waves.

• Surface Distribution: Charges reside on the outer surface of conductors due to repulsive forces.

• Quantization of Charge: Charge can only exist in integral multiples of the charge of an electron (e).

1.3 Comparison of Charge and Mass

• Charge can be positive, negative, or zero; mass is always positive.

• Charge is independent of body velocity; mass increases with velocity.

• Charge is quantized; quantization of mass is not established.

• Charge is always conserved; mass can be converted to energy.

• Forces between charges can be attractive or repulsive; gravitational forces are always attractive.

1.4 Methods of Charging

• By Friction: Charging occurs when two bodies are rubbed together, resulting in electron transfer (e.g., glass rod and silk).

• By Induction: Opposite charges are attracted when a charged body is brought near an uncharged body.

• By Conduction: Charging occurs when two conductors are brought into contact, and charge distributes over both.

2. Coulomb's Law

• Describes the force between two point charges separated by a distance.

• Mathematical Form: F = k * (Q1 * Q2) / r^2, where k is Coulomb's constant.

• Characteristics:

  • The force is along the line connecting the charges.

  • Like charges repel, opposite charges attract.

  • It is a conservative force and follows the inverse square law.

2.1 Variation of Constant

• Coulomb's constant varies based on the medium between charges.

• For air: k = 9.0 × 10^9 N m^2/C^2.

3. Electric Field

• Defined as the space around a charge in which another charged particle experiences a force.

3.1 Electric Field Intensity

• Defined as the force per unit positive charge at a point.

• S.I. Unit: Newton/Coulomb (N/C)

• Direction: Away from positive charges, towards negative charges.

3.2 Superposition of Electric Fields

• Resultant electric field is the vector sum of fields from multiple charges.

3.3 Continuous Charge Distributions

• Charge density types:

  • Linear charge density (lambda, λ): charge/length (C/m).

  • Surface charge density (sigma, σ): charge/area (C/m^2).

  • Volume charge density (rho, ρ): charge/volume (C/m^3).

4. Electric Dipole

• A dipole consists of two equal and opposite charges separated by a distance.

• Dipole Moment (p): Defined as the product of charge magnitude and distance (p = q * d).

• Unit: Coulomb-meter (C*m) or Debye.

• Electric Potential and Field due to a Dipole:

  • V = (p * cos(θ)) / (4 * π * ε_0 * r^2)

  • Electric fields in the dipole are calculated using similar relationships.

5. Gauss's Law

• Definition: Total electric flux through a closed surface equals the charge enclosed divided by the permittivity of free space.

• Mathematical Representation: Φ = Q_enclosed / ε_0

• Applications: Used for calculating electric fields due to symmetric charge distributions (lines, sheets, and spheres).

6. Neutral Point

• Defined as the point where the resultant electric field is zero, typically between two like or opposite charges depending on their magnitudes and positions.

7. Equilibrium of Charge

• A charge is in equilibrium if the net force acting on it is zero.

• Types of Equilibrium:

  • Stable: Returns to equilibrium post-displacement.

  • Unstable: Moves further away post-displacement.

  • Neutral: Remains in place post-displacement.

8. Electric Field due to a Dipole

• Detailed understanding of how to calculate the electric field from dipoles, including various configurations, ensuring understanding of concepts such as torque in uniform electric fields, stability, and potential energies.