Physics Class 12 Chapter 1 Notes: Electric Charges and Fields
Comprehensive Guide with Formulas, Diagrams & Examples
1. Electric Charge
Basic Concepts
- Definition: A fundamental property of matter that causes it to experience electromagnetic force.
- Types:
- Positive Charge (Protons)
- Negative Charge (Electrons)
- SI Unit: Coulomb (C)
- Properties:
- Quantized (\(e = 1.6 \times 10^{-19} \, \text{C}\))
- Conserved (cannot be created/destroyed)
- Additive (like charges repel, unlike attract)
Methods of Charging
- Friction: Rubbing two objects (e.g., glass rod with silk).
- Conduction: Direct contact with a charged object.
- Induction: Charging without contact (polarization).
2. Coulomb's Law
Mathematical Form
\[ F = k \frac{|q_1 q_2|}{r^2} \]- k (Coulomb's Constant): \(9 \times 10^9 \, \text{Nm}^2/\text{C}^2\)
- Permittivity of Free Space (\(\epsilon_0\)): \(8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2\)
- Force Direction:
- Repulsive for like charges.
- Attractive for unlike charges.
Example
Two charges \(q_1 = 2 \, \mu\text{C}\) and \(q_2 = -3 \, \mu\text{C}\) are 0.1 m apart. Calculate the force.
Solution:
\[ F = 9 \times 10^9 \frac{|2 \times 10^{-6} \times -3 \times 10^{-6}|}{(0.1)^2} = 5.4 \, \text{N} \, (\text{attractive}) \]3. Electric Field & Field Lines
Definition
- Electric Field (E): Force per unit test charge (\(E = F/q_0\)).
- SI Unit: N/C or V/m.
Field Due to Point Charge
\[ E = k \frac{|q|}{r^2} \]Direction:
- Radially outward for +ve charge.
- Radially inward for -ve charge.
Electric Field Lines
- Properties:
- Never intersect.
- Density ∝ Field strength.
- Start from +ve, end at -ve charge.
4. Electric Flux & Gauss's Law
Electric Flux (\(\phi_E\))
\[ \phi_E = E \cdot A \cos \theta \]where θ is the angle between E and normal to the surface.
Gauss's Law
\[ \phi_E = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]Applications:
- Infinite Plane Sheet: \(E = \frac{\sigma}{2\epsilon_0}\)
- Conducting Sphere: \(E = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}\)
5. Electric Dipole
Definition
Two equal and opposite charges (\(+q\) and \(-q\)) separated by distance \(2a\).
Dipole Moment (\(\vec{p}\))
\[ \vec{p} = q \times 2\vec{a} \]Direction: From \(-q\) to \(+q\).
Field Due to Dipole
- Axial Line: \[ E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3} \]
- Equatorial Line: \[ E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3} \]
6. Continuous Charge Distribution
Types
- Linear Charge Density (\(\lambda\)): \(\lambda = \frac{dq}{dl}\)
- Surface Charge Density (\(\sigma\)): \(\sigma = \frac{dq}{dA}\)
- Volume Charge Density (\(\rho\)): \(\rho = \frac{dq}{dV}\)
7. Important Derivations
- Torque on Dipole in Uniform Field: \[ \tau = pE \sin \theta \]
- Potential Energy of Dipole: \[ U = -pE \cos \theta \]
8. NCERT vs. Board Exam Focus
| NCERT Concepts | Important for Exams |
|---|---|
| Coulomb's Law | Numerical Problems |
| Gauss's Law | Derivation + Applications |
| Electric Dipole | Diagrams + Torque Formula |
| Field Lines | Properties (VVI for MCQ) |
9. Common FAQs
Q1. What is the SI unit of electric flux?
Ans: Volt-meter (V·m) or Nm²/C.
Q2. Why do electric field lines never cross?
Ans: Because the field direction must be unique at any point.
Q3. How is Gauss's law useful?
Ans: Simplifies calculation of E for symmetric charge distributions.
Final Tips for Exams
- ✔️ Practice numericals from NCERT Examples.
- ✔️ Revise field line patterns (dipole, plane sheet, etc.).
- ✔️ Memorize Gauss's law applications.
Physics Class 12 Chapter 1 Notes: Electric Charges and Fields
Comprehensive Guide with Formulas, Diagrams & Examples
1. Electric Charge
Basic Concepts
- Definition: A fundamental property of matter that causes it to experience electromagnetic force.
- Types:
- Positive Charge (Protons)
- Negative Charge (Electrons)
- SI Unit: Coulomb (C)
- Properties:
- Quantized (\(e = 1.6 \times 10^{-19} \, \text{C}\))
- Conserved (cannot be created/destroyed)
- Additive (like charges repel, unlike attract)
Methods of Charging
- Friction: Rubbing two objects (e.g., glass rod with silk).
- Conduction: Direct contact with a charged object.
- Induction: Charging without contact (polarization).
2. Coulomb’s Law
Mathematical Form
\[
F = k \frac{|q_1 q_2|}{r^2}
\]
- k (Coulomb’s Constant): \(9 \times 10^9 \, \text{Nm}^2/\text{C}^2\)
- Permittivity of Free Space (\(\epsilon_0\)): \(8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2\)
- Force Direction:
- Repulsive for like charges.
- Attractive for unlike charges.
Example
Two charges \(q_1 = 2 \, \mu\text{C}\) and \(q_2 = -3 \, \mu\text{C}\) are 0.1 m apart. Calculate the force.
Solution:
\[
F = 9 \times 10^9 \frac{|2 \times 10^{-6} \times -3 \times 10^{-6}|}{(0.1)^2} = 5.4 \, \text{N} \, (\text{attractive})
\]
3. Electric Field & Field Lines
Definition
- Electric Field (E): Force per unit test charge (\(E = F/q_0\)).
- SI Unit: N/C or V/m.
Field Due to Point Charge
\[
E = k \frac{|q|}{r^2}
\]
Direction:
- Radially outward for +ve charge.
- Radially inward for -ve charge.
Electric Field Lines
- Properties:
- Never intersect.
- Density ∝ Field strength.
- Start from +ve, end at -ve charge.
4. Electric Flux & Gauss’s Law
Electric Flux (\(\phi_E\))
\[
\phi_E = E \cdot A \cos \theta
\]
where θ is the angle between E and normal to the surface.
Gauss’s Law
\[
\phi_E = \frac{Q_{\text{enclosed}}}{\epsilon_0}
\]
Applications:
- Infinite Plane Sheet: \(E = \frac{\sigma}{2\epsilon_0}\)
- Conducting Sphere: \(E = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}\)
5. Electric Dipole
Definition
Two equal and opposite charges (\(+q\) and \(-q\)) separated by distance \(2a\).
Dipole Moment (\(\vec{p}\))
\[
\vec{p} = q \times 2\vec{a}
\]
Direction: From \(-q\) to \(+q\).
Field Due to Dipole
- Axial Line:
\[
E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}
\] - Equatorial Line:
\[
E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}
\]
6. Continuous Charge Distribution
Types
- Linear Charge Density (\(\lambda\)): \(\lambda = \frac{dq}{dl}\)
- Surface Charge Density (\(\sigma\)): \(\sigma = \frac{dq}{dA}\)
- Volume Charge Density (\(\rho\)): \(\rho = \frac{dq}{dV}\)
7. Important Derivations
- Torque on Dipole in Uniform Field:
\[
\tau = pE \sin \theta
\] - Potential Energy of Dipole:
\[
U = -pE \cos \theta
\]
8. NCERT vs. Board Exam Focus
| NCERT Concepts | Important for Exams |
|---|---|
| Coulomb’s Law | Numerical Problems |
| Gauss’s Law | Derivation + Applications |
| Electric Dipole | Diagrams + Torque Formula |
| Field Lines | Properties (VVI for MCQ) |
9. Common FAQs
Q1. What is the SI unit of electric flux?
Ans: Volt-meter (V·m) or Nm²/C.
Q2. Why do electric field lines never cross?
Ans: Because the field direction must be unique at any point.
Q3. How is Gauss’s law useful?
Ans: Simplifies calculation of E for symmetric charge distributions.
Final Tips for Exams
- ✔️ Practice numericals from NCERT Examples.
- ✔️ Revise field line patterns (dipole, plane sheet, etc.).
- ✔️ Memorize Gauss’s law applications.