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Coulomb's Law describes how electric forces operate between electric charges. It tells us that the force between two point charges is directly proportional to the product of the magnitudes of these charges. It is also inversely proportional to the square of the distance between them.
This means:

• If the charges increase, the force increases.
• If the distance increases, the force decreases.

The law can be expressed with the formula:\[F = k \frac{q_1 q_2}{r^2}\]where:

• \( F \) is the electrostatic force.
• \( k \) is Coulomb's constant \((8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2)\).
• \( q_1 \) and \( q_2 \) are the charges.
• \( r \) is the distance between the charges.

This fundamental law is the basis for understanding how charges interact and plays a crucial role in calculating electric potential and fields.

A point charge is an idealized model of a charge that is infinitely small yet still exerts a force. In practice, it represents an electric charge at a single point in space.
Point charges are useful in simplifying calculations and understanding electric fields, especially when dealing with symmetrical situations.

• Consider a charge at a definite location, with no physical extent.
• Its electric field influences other charges around it regardless of its physical size.

The potential due to a point charge is calculated using the equation:\[V = \frac{k \cdot q}{r}\]where:

• \( V \) is the electric potential at a distance \( r \) from the charge \( q \).
• \( k \) is Coulomb's constant.
• \( r \) is the distance from the charge to the point of interest.

This model helps us understand the contributions of each charge in a configuration, like the four charges at the corners of a square.

The electric field is a region around a charged object where a force would be exerted on other charges. Its strength and direction are defined by a vector quantity showing how a positive test charge would move.
It can be described using the formula:\[E = \frac{F}{q}\]where:

• \( E \) is the electric field.
• \( F \) is the force experienced.
• \( q \) is the charge witnessing the force.

Electric fields have some key characteristics:

• They point away from positive charges and toward negative charges.
• The closer you are to a charge, the stronger the field.
• Fields can superimpose; when multiple charges are present, the total field is the vector sum of individual fields.

The electric potential relates to the work done moving a charge within this field. It highlights the relationship between the potential energy and electric field in charge configurations.

The Pythagorean theorem is a mathematical principle that relates the lengths of the sides of a right triangle. It is essential in calculating distances in physics, such as those from the corners of a square to its center.
The theorem states:\[c^2 = a^2 + b^2\]where:

• \( c \) is the length of the hypotenuse.
• \( a \) and \( b \) are the lengths of the other two sides.

In the context of the square, the diagonal is considered the hypotenuse, and the sides are the other two sides.
Using this theorem, if each side of the square is 0.3 m, the diagonal \( d \) is:\[d = \sqrt{0.3^2 + 0.3^2} = 0.3\sqrt{2}\]This helps us find the distance from each corner to the center as half the diagonal:\[r = \frac{d}{2} = \frac{0.3\sqrt{2}}{2} = 0.212 \, \text{m}\]By understanding this distance, we can calculate the electric potential at that point from the charges.