Electric Charges and Fields Class 12 Notes: Complete Physics Guide

Fundamentals of Electric Charges

Electric charges are the basic property of matter responsible for electric forces. There are two types of charges: positive and negative. Like charges repel, while unlike charges attract each other.

Key points:

• Charge is quantized in multiples of the elementary charge $e = 1.6 \times 10^{-19}$ coulombs.
• Charge is conserved; it cannot be created or destroyed.
• Conductors allow free movement of charges, whereas insulators do not.

Example: If an object gains 3 extra electrons, its charge is $3 \times (-1.6 \times 10^{-19}) = -4.8 \times 10^{-19}$ C.

Coulomb’s Law: Force Between Point Charges

Coulomb’s law quantifies the force between two point charges:

$$F = k \frac{|q_1 q_2|}{r^2}$$

Where:

• $F$ is the magnitude of force,
• $q_1$ and $q_2$ are the charges,
• $r$ is the distance between charges,
• $k = 9 \times 10^9$ Nm²/C² (Coulomb constant).

The force acts along the line joining the charges and is repulsive if charges are alike and attractive if opposite.

Worked example: Two charges of +2 μC and -3 μC are 0.5 m apart. Find the force between them.

$$F = 9 \times 10^9 \times \frac{2 \times 10^{-6} \times 3 \times 10^{-6}}{(0.5)^2} = 216 \text{ N (attractive)}$$

Electric Field and Its Properties

The electric field $\vec{E}$ at a point is the force experienced per unit positive charge placed at that point:

$$\vec{E} = \frac{\vec{F}}{q}$$

It is a vector quantity with direction away from positive charges and toward negative charges.

The electric field due to a point charge $Q$ at distance $r$ is:

$$E = k \frac{|Q|}{r^2}$$

Key properties:

• Electric field lines never intersect.
• Field lines start on positive charges and end on negative charges.
• The density of lines indicates field strength.

Example: Calculate the electric field 0.2 m from a charge of +5 μC.

$$E = 9 \times 10^9 \times \frac{5 \times 10^{-6}}{(0.2)^2} = 1.125 \times 10^6 \, \text{N/C}$$

Electric Field Lines and Their Significance

Electric field lines visually represent the electric field around charges.

Characteristics:

• Lines originate from positive charges and terminate at negative charges.
• The number of lines is proportional to the magnitude of the charge.
• Lines never cross each other.
• The closer the lines, the stronger the electric field.

Comparison Table: Electric Field Lines vs Magnetic Field Lines

Understanding field lines helps in visualizing forces on charges and predicting charge movement.

Electric Flux and Gauss’s Law

Electric flux $\Phi_E$ measures the number of electric field lines passing through a surface:

$$\Phi_E = \vec{E} \cdot \vec{A} = EA \cos \theta$$

Where:

• $E$ is the electric field,
• $A$ is the area of the surface,
• $\theta$ is the angle between $\vec{E}$ and the normal to the surface.

Gauss’s Law: The total electric flux through a closed surface equals the net charge enclosed divided by the permittivity of free space $\epsilon_0$:

$$\Phi_E = \frac{Q_{\text{enclosed}}}{\epsilon_0}$$

This law simplifies electric field calculations for symmetric charge distributions.

Example: For a point charge $Q$ at the centre of a spherical surface of radius $r$, the electric flux is:

$$\Phi_E = E \times 4 \pi r^2 = \frac{Q}{\epsilon_0}$$

Hence,

$$E = \frac{Q}{4 \pi \epsilon_0 r^2}$$

Important Formulas Summary

Here is a quick summary of key formulas from the Electric Charges and Fields chapter:

Make sure to practice problems using these formulas for better exam readiness.