Question

Two positive point charges ${q_1}$ and ${q_2}$ are kept at a distance d. If the distance between them is triple. Calculate by which factor new electrostatic force is decreased.
$
  (a){\text{ 3}} \\
  (b){\text{ 6}} \\
  (c){\text{ 8}} \\
  (d){\text{ 9}} \\
  (e){\text{ 12}} \\
 $

Answer 1

Hint – In this question use the direct formula for coulomb’s law of electrostatics that is $F = \dfrac{1}{{4\pi {\xi _0}}}\dfrac{{{q_1}{q_2}}}{{{d^2}}}$, since the distance is tripled this force has inverse square dependency over the distance. Hence with the new distance write the new force and find its relation with the force when the distance is d.

Complete step-by-step answer:
The Coulomb Law states:
'The magnitude of the attraction or repulsion electrostatic force between two point charges is directly proportional to the sum of the magnitudes of charges and inversely proportional to the distance square between them.'
The force is along the straight line joining them.
If the two charges have the same sign, the electrostatic force between them is repulsive.
If they have different signs, the force between them is attractive.
Now it is given that two point charges are ${q_1}$ and${q_2}$.
And the distance between them is (d).
So the electrostatic force between them is
$ \Rightarrow F = \dfrac{1}{{4\pi {\xi _0}}}\dfrac{{{q_1}{q_2}}}{{{d^2}}}$......... (1),
Where $\dfrac{1}{{4\pi {\xi _0}}}$ is proportionality constant whose value is$9 \times {10^9}{\text{ }}\dfrac{{{\text{N}}{{\text{m}}^2}}}{{{{\text{C}}^2}}}$.
Now if the distance between the point charges are triple then the distance (${d_1}$) become,
$ \Rightarrow {d_1} = 3d$
Now let the new force between these two point charges are ${F_1}$
$ \Rightarrow {F_1} = \dfrac{1}{{4\pi {\xi _0}}}\dfrac{{{q_1}{q_2}}}{{{{\left( {3d} \right)}^2}}} = \dfrac{1}{{4\pi {\xi _0}}}\dfrac{{{q_1}{q_2}}}{{9{d^2}}}$
Now from equation (1) we have,
$ \Rightarrow {F_1} = \dfrac{F}{9}$
So the new force is decreased by 9 times.
So this is the required answer.
Hence option (D) is the correct answer.

Note – Coulomb’s law is not valid only too positive or like charges, or negative charges only. It is also valid if two charges are of opposite signs to each other. If the charge pair is positive and negative then the negative sign is put into the direct formula and the negative sign shows the force of attraction.