Electric Charges and Fields Class 12 Notes for CBSE Physics Exam

Understanding Electric Charges: Basics and Properties

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges: positive and negative. Like charges repel each other, while unlike charges attract.

Key properties of electric charges include:

• Quantization: Charge exists in discrete amounts, multiples of the elementary charge $e = 1.6 \times 10^{-19}$ coulombs.
• Conservation: Total electric charge in an isolated system remains constant.
• Additivity: Net charge is the algebraic sum of individual charges.

Charges can be transferred by friction, conduction, or induction. Conductors allow free movement of charges, whereas insulators do not.

Example:

If an object gains $3 \times 10^{18}$ electrons, its net charge is:

$$Q = n \times e = 3 \times 10^{18} \times (-1.6 \times 10^{-19}) = -0.48 \text{ C}$$

This negative charge means the object has excess electrons.

Coulomb’s Law: Force Between Two Point Charges

Coulomb’s law quantifies the electrostatic force between two point charges. It states:

> The magnitude of force $F$ between two charges $q_1$ and $q_2$ separated by distance $r$ is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Mathematically:

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

where $k = \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$ and $\epsilon_0$ is the permittivity of free space.

Direction: Force acts along the line joining the charges. It is repulsive if charges are alike and attractive if unlike.

Worked Example:

Two charges, $+2 \mu C$ and $-3 \mu C$, are 0.5 m apart. Find the force between them.

$$F = 9 \times 10^9 \times \frac{2 \times 10^{-6} \times 3 \times 10^{-6}}{(0.5)^2} = 0.216 \text{ N}$$

The force is attractive since charges are opposite.

Electric Field: Definition and Calculation

An electric field is a region around a charged object where another charge experiences an electric force. It is a vector quantity.

Definition: Electric field $\vec{E}$ at a point is the force $\vec{F}$ experienced by a positive test charge $q$ placed at that point divided by the magnitude of the charge.

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

Units: Newton per Coulomb (N/C).

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

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

Direction: Away from positive charge, towards negative charge.

Superposition Principle: The net electric field due to multiple charges is the vector sum of the fields due to individual charges.

Example:

Calculate the electric field 0.2 m from a $+5 \mu C$ charge.

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

Electric Field Lines and Their Properties

Electric field lines visually represent the direction and strength of an electric field.

Key properties:

• Lines start from positive charges and end on negative charges.
• The number of lines is proportional to the magnitude of the charge.
• Lines never intersect.
• The density of lines indicates field strength; closer lines mean stronger field.
• Field lines are perpendicular to the surface of a conductor.

Comparison Table: Electric Field Lines vs Equipotential Surfaces

Understanding these helps in visualizing electric fields and solving related problems.

Gauss’s Law and Its Applications

Gauss’s law states:

> The total electric flux through a closed surface is equal to $\frac{1}{\epsilon_0}$ times the net charge enclosed within the surface.

Mathematically:

$$\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\epsilon_0}$$

where $\Phi_E$ is the electric flux, $\vec{E}$ is the electric field, and $d\vec{A}$ is the area element vector.

Applications:

• Calculating electric fields of symmetric charge distributions (spheres, cylinders, planes).
• Deriving the electric field outside and inside a charged conductor.

Example:

For a uniformly charged sphere of radius $R$ and total charge $Q$, the electric field outside ($r > R$) is:

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

Inside ($r < R$), the field is zero for a conductor.

Gauss’s law simplifies complex calculations by exploiting symmetry.

Summary of Important Formulas in Electric Charges and Fields

Here is a quick reference table of key formulas:

Use these formulas with proper units and directions for solving NCERT problems effectively.