Two charges in polygon Example with exercise

Hello, science enthusiast! In this exercise, my friend the reader will demonstrate how to calculate the electric force between two objects in a polygon using the Law of Coulomb. It's important to keep in mind that this is only a simplified version of more complicated situations in which the loads may be distributed irrationally or in three dimensions, but the fundamentals of Coulomb's law still hold true.

Finding the location of the load: You must first know the coordinates or location of the load on a polygon. This enables him to determine their distance from one another.

Now we can calculate the distance between the charges: Use the formula for the distance between two points in a plane (usually in Cartesian coordinates) to find the distance between the two charges. If there are two charges at points A(x1, y1) and B(x2, y2), the distance (d) between them is calculated as follows:

d = √((x2 - x1)² + (y2 - y1)²)

We already have this information, dear readers and lovers of science, you must know the magnitude of each of the charges, which is measured in coulombs (C).

Use Coulomb's Law: Coulomb's Law describes the electric force between two point charges and is expressed as:

F = k * (|q1 * q2|) / d²

Where:

F is the electric force between the two charges (in newtons, N).

k is Coulomb's constant, which has a value of approximately 8.99 x 10^9 N•m²/C² in a vacuum.

q1 and q2 are the magnitudes of the two charges (in coulombs, C).

d is the distance between the charges (in meters, m).

This point is more interesting, since we have to calculate the electric force, we have to: Substitute the known values in the Coulomb's Law equation and calculate the electric force between the two charges.

It is worth noting that this description applies to one-time charges that are on board an aircraft. If the load has a continuous load distribution, or if you are working in three dimensions, the calculations can become more complicated and require integration rather than simple addition.

Suppose we have two point charges, q1 = 4 x 10^(-6) C and q2 = -2 x 10^(-6) C, located in a polygon with the following coordinates in the Cartesian coordinate system:

Charge q1 is at point A(2 m, 3 m).

Charge q2 is at point B(-1 m, 2 m).

We apply the following:

d = √((x2 - x1)² + (y2 - y1)²)

Where:

x1, y1 are the coordinates of the charge q1.
x2, y2 are the coordinates of the charge q2.
d = √((-1m - 2m)² + (2m - 3m)²)
d = √((-3m)² + (-1m)²)
d = √(9 m² + 1 m²)
d = √(10 m²)
d = 10m

Now that we know the distance between the two charges (d = 10 m), we can use Coulomb's law to calculate the electric force between them:

F = k * (|q1 * q2|) / d²

Where:

k is the Coulomb constant (8.99 x 10^9 N•m²/C²).

q1 and q2 are the magnitudes of the two charges (q1 = 4 x 10^(-6) C, q2 = -2 x 10^(-6) C).

d is the distance between the charges (d = 10 m).

F = (8.99 x 10^9 N•m²/C²) * (|4 x 10^(-6) C * -2 x 10^(-6) C|) / (10 m)²
F = (8.99 x 10^9 N•m²/C²) * (8 x 10^(-12) C²) / (100 m²)
F = (7.192 x 10^(-2) N) / 100 m²
F = 7.192 x 10^(-4)N

We have as a result, a lover of science and tax, the electric force between these two polygonal charges is approximately 7,192 x 10^(-4) N.

Bibliographic Reference
Introduction to the equations of mathematical physics
By Andrei Giniatoulline, 2011.