In the previous post, we discussed the basics of electric fields and how they are represented by field lines. In this post, we will dive into the mathematics behind calculating the magnitude and direction of an electric field produced by a point charge.

To calculate the electric field at a specific point due to a point charge, we use Coulomb's law: E = k * (Q / r^2), where E is the electric field, k is the Coulomb's constant (k ≈ 9 × 10^9 Nm^2/C^2), Q is the charge of the point charge, and r is the distance between the charge and the point in question.

Let's consider an example to illustrate this concept. Suppose we have a positive point charge with a charge of +2 μC located 0.5 meters away from a point P. We can use Coulomb's law to calculate the electric field at point P as follows: E = (9 × 10^9 Nm^2/C^2) * (2 × 10^-6 C) / (0.5^2 m^2). With simple calculations, we find that the electric field at point P is 7.2 × 10^6 N/C, directed away from the positive charge.

It is important to note that the electric field is a vector quantity and has both magnitude and direction. The magnitude is given by Coulomb's law, and the direction is determined by the nature of the charge (+ or -). The electric field vector points away from a positive charge and towards a negative charge.

By knowing the electric field at a point due to a single charge, we can also calculate the net electric field at that point if there are multiple charges. In such cases, the electric fields due to individual charges can be added up vectorially to find the resultant electric field at the point.