Electrostatics is the branch of physics that deals with the charges that are either not in motion or are very slow-moving. For instance, the charges that attract two balloons are very slow and are an example of electrostatics.
The observations made in the 18th century, such as charges either attract each other or get repealed or the decreasing distance between charges increases, gave rise to Coulomb’s Law of Electrostatics. The law stands to be the first explanation and identification of electrostatics. It stands as the fundamentals for the derivation of other laws, such as Gauss’ Law.
In the below information, there will be the elucidation of what electrostatics is. Further, there will be a complete derivation of Coulomb’s law for electrostatic charges and it’s working for various quantities. Better understanding will be interpreted with practical examples of electrostatic forces.
What exactly is Electrostatics?
Electrostatics is the branch of physics that deals with stationary or slow-moving charges; for instance, when the paper attracts a ruler, the force is weak and shaky. Here, there are electrostatic charges that hold the paper to the ruler. At the same time, the force is weak and can break off easily. The phenomenon that occurred by these charges is described by Coulomb’s Law theoretically.
Coulomb’s Law
Coulomb’s law defines the electrostatic forces in terms of repulsion and attraction. It is a kind of inverse square law, like the gravitational force. Coulomb’s law of electrostatics states that the magnitude at which electrostatic charges repel or attract is “directly proportionate” to the magnitude of charges when multiplied. It is also proportionally inverse to the square distance between the charges.
Let us now get to the derivation of Coulomb’s Law, shall we? The derivation will help in understanding how the law is implemented mathematically.
Let q1 and q2 be the two-point charges. q1 is the source charge, and q2 is the test charge. And r is the distance between the point charges.
F gives the force of attraction/repulsion between the two point charges.
Thus,
F ∝ q1q2
And, F ∝ 1/r2
Therefore, we can say that –
F = k q1q2/ r2
Where k is the constant for proportionality equal to 1/4 π ε0, it presents the vacuum’s ability to store electric energy. The value of k results in 9 × 109 Nm2/ C2. As we consider the S.I. unit for ε0 value, it is calculated as 8.854 × 10-12 C2 N-1 m-2.
Vector form of Coulomb’s Law
Let us consider two charges, q1 and q2, at r1 and r2, to be their position vectors, respectively.
Since they have similar charges, they won’t get attracted to one another.
Let the force of q1 on q2, be F12 and the force of q2 on q1 be F21.
Therefore, the vector from q1 to q2 is r12.
r21 = r2 – r1
