3. State Coulomb's law of electrostatic force in
vector form. Find the force between one election
and 2 proton are kept at a distance of 2m
in (i) air (ii) Water
Answers
Coulomb’s Law
Coulomb’s Law gives an idea about the force between two point charges. By the word point charge, we mean that in physics, the size of linear charged bodies is very small as against the distance between them. Therefore, we consider them as point charges as it becomes easy for us to calculate the force of attraction/ repulsion between them.
Coulomb's Law
Charles-Augustin de Coulomb, a French physicist in 1784, measured the force between two point charges and he came up with the theory that the force is inversely proportional to the square of the distance between the charges. He also found that this force is directly proportional to the product of charges (magnitudes only).
We can show it with the following explanation. Let’s say that there are two charges q1 and q2. The distance between the charges is ‘r’, and the force of attraction/repulsion between them is ‘F’. Then
F ∝ q1q2
Or, F ∝ 1/r2
F = k q1q2/ r2
where k is proportionality constant and equals to 1/4 π ε0. Here, ε0 is the epsilon naught and it signifies permittivity of a vacuum. The value of k comes 9 × 109 Nm2/ C2 when we take the S.I unit of value of ε0 is 8.854 × 10-12 C2 N-1 m-2.
According to this theory, like charges repel each other and unlike charges attract each other. This means charges of same sign will push each other with repulsive forces while charges with opposite signs will pull each other with attractive force.
Vector Form of Coulomb’s Law
The physical quantities are of two types namely scalars (with the only magnitude) and vectors (those quantities with magnitude and direction). Force is a vector quantity as it has both magnitude and direction. The Coulomb’s law can be re-written in the form of vectors. Remember we denote the vector “F” as F, vector r as r and so on.
Let there be two charges q1 and q2, with position vectors r1 and r2 respectively. Now, since both the charges are of the same sign, there will be a repulsive force between them. Let the force on the q1 charge due to q2 be F12 and force on q2 charge due to q1 charge be F21. The corresponding vector from q1 to q2 is r21 vector.
r21 = r2 – r1
To denote the direction of a vector from position vector r1 to r2 , and from r2 to r1 as:
Now, the force on charge q2 due to q1, in vector form is:
The above equation is the vector form of Coulomb’s Law.