91Ó°ÊÓ

In an electric field, when a charge is moved from one point to another, work is done.This is because a force acts on the charge due to the electric field.
The work done, denoted as \( W \), when moving the charge depends on several factors:

• The strength of the electric field, \( E \).
• The magnitude of the charge, \( q \).
• The distance the charge is moved along the direction of the field, \( d \).
• The angle between the field and the path of movement.

The fundamental formula to calculate the work done in an electric field is:\[W = E \cdot q \cdot d \cdot \cos(\theta)\]Here, \( \theta \) is the angle between the direction of the electric field and the direction of movement.
In simpler terms, if a charge is moved directly along the electric field lines, \( \theta = 0^{\circ} \) making \( \cos(\theta) = 1 \). Therefore, full work is done. However, if the charge moves perpendicular to the electric field lines, \( \theta = 90^{\circ} \), making \( \cos(\theta) = 0 \). In this case, no work is done as there is no displacement along the field direction.

Every object is made of atoms, and atoms consist of protons, neutrons, and electrons.
Out of these, protons have a positive charge, and electrons have a negative charge.Electric charge is an intrinsic property of certain subatomic particles. This property allows them to exert force and interact through electric fields.
Charge, denoted by \( q \), is measured in coulombs (C).
There are two types of electric charge, positive and negative:

• Like charges repel each other.
• Opposite charges attract each other.

A charged object will always interact with another charged object through the presence of an electric field, exerting forces without direct contact.
In our exercise, the charge value provided is \( 0.2 \ ext{C} \), which is quite substantial compared to common experimental charges such as microcoulombs (\( \mu C \)). Recognizing the magnitude of the charge helps to understand its influence within electric fields.

Coulomb's Law is a fundamental principle of electromagnetism detailing how electric charges interact with one another.
It quantifies the amount of force between two stationary, charged objects.The force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:\[F = k \cdot \frac{|q_1 \cdot q_2|}{r^2}\]Where:

• \( k \) is the Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)
• \( |q_1 \cdot q_2| \) denotes the absolute product of the magnitudes of the charges
• \( r \) is the distance between the charges

Coulomb's law shows us that the force is both dependent on the magnitude of the charges and inversely proportional to the square of the distance between them.This means that as charges move further apart, the force exponentially decreases, and as they get closer, the force increases substantially.
Therefore, understanding the driving principles behind Coulomb's Law provides us with insight into how electric charges behave within and outside electric fields.