What is Electric Charges and Fields Class 12: Complete Guide

Definition and Types of Electric Charges

Electric charge is a fundamental property of particles that causes them to experience a force in an electric field. There are two types of charges:

• Positive charge (+): Carried by protons.
• Negative charge (−): Carried by electrons.

Key properties of electric charges:

• Charges are quantized, meaning charge exists in discrete amounts of $e = 1.6 \times 10^{-19}$ coulombs.
• Charge is conserved; it cannot be created or destroyed.
• Like charges repel each other, unlike charges attract.

In Class 12 NCERT Physics, understanding these properties helps explain electric interactions at the microscopic level.

Coulomb’s Law: Force Between Electric Charges

Coulomb’s law describes 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.

Mathematically:

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

Where:

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

Direction: The force is along the line joining the charges, repulsive if charges are like, attractive if unlike.

Worked Example:

Two charges, +3 µC and -2 µC, are 0.5 m apart. Calculate the force between them.

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

The force is attractive.

Electric Field: Concept and Definition

An electric field is a region around a charged object where other charges experience an electric force.

Definition: Electric field $\vec{E}$ at a point is defined as the force $\vec{F}$ experienced by a small positive test charge $q_0$ placed at that point divided by the magnitude of the test charge:

$$ \vec{E} = \frac{\vec{F}}{q_0} $$

• Electric field is a vector quantity.
• Its SI unit is newton per coulomb (N/C).

Important points:

• The test charge $q_0$ should be very small to avoid disturbing the original field.
• The direction of $\vec{E}$ is the direction of force on a positive test charge.

Electric fields help us understand how charges influence space around them.

Electric Field Due to a Point Charge

The electric field created by a single point charge $q$ at a distance $r$ from it is given by:

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

• The field points radially outward if $q$ is positive.
• The field points radially inward if $q$ is negative.

Vector form:

$$ \vec{E} = k \frac{q}{r^2} \hat{r} $$

Where $\hat{r}$ is the unit vector from the charge to the point.

Example:

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

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

This field points away from the charge.

Electric Field Lines and Their Properties

Electric field lines visually represent the electric field. Key properties:

• Lines start on positive charges and end on negative charges.
• The number of lines is proportional to the magnitude of the charge.
• Lines never cross.
• The density of lines indicates the strength of the field.

These lines help visualize forces and field patterns around charges.

Comparison: Electric Charge vs Electric Field

Understanding the difference between electric charge and electric field is crucial:

This comparison clarifies their roles in electrostatics.