Question

Point charges ${{\text{q}}_1}$ and ${{\text{q}}_2}$ are placed in air at a distance ‘r’. What is the ratio of the force on charge ${{\text{q}}_1}$ by charge ${{\text{q}}_2}$ and force on charge ${{\text{q}}_2}$ by charge ${{\text{q}}_1}$?
$
  {\text{A}}{\text{. }}\dfrac{{{{\text{q}}_1}}}{{{{\text{q}}_2}}} \\
  {\text{B}}{\text{. }}\dfrac{{{{\text{q}}_2}}}{{{{\text{q}}_1}}} \\
  {\text{C}}{\text{. 1}} \\
  {\text{D}}{\text{. }}{\left( {\dfrac{{{{\text{q}}_1}}}{{{{\text{q}}_2}}}} \right)^2} \\
 $

Answer 1

Hint: Here, we will proceed by writing down the simple formula given by coulomb’s law. Then, we will consider two cases i.e., both charges are unlike in nature and both charges are like in nature.
Formula used:
${\text{F}} = \dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}$.
According to Coulomb’s law,
Electrostatic force, ${\text{F}} = \dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}{\text{ }} \to {\text{(1)}}$ where ${{\text{q}}_1}$ and ${{\text{q}}_2}$ are two point charges and separated by a distance r and K is Coulomb’s constant

Complete answer:
${{\text{q}}_1}$ and ${{\text{q}}_2}$ are opposite i.e., either ${{\text{q}}_1}$ is a positive charge and ${{\text{q}}_2}$ is a negative charge or ${{\text{q}}_1}$ is a negative charge and ${{\text{q}}_2}$ is a positive charge. The electrostatic force will be repulsive if the signs of these two points charges ${{\text{q}}_1}$ and ${{\text{q}}_2}$ are same i.e., either both point charges have positive charges or both point charges have negative charges.
As shown in the both figures, ${{\text{F}}_{12}}$ denotes the electrostatic force acting on charge ${{\text{q}}_1}$ by charge ${{\text{q}}_2}$ and ${{\text{F}}_{21}}$ denotes the electrostatic force acting on charge ${{\text{q}}_2}$ by charge ${{\text{q}}_1}$.
For both the cases, using formula given in equation (1) we have
Force on charge ${{\text{q}}_1}$ by charge ${{\text{q}}_2}$ ${{\text{F}}_{12}} = \dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}{\text{ }} \to {\text{(2)}}$
Force on charge ${{\text{q}}_2}$ by charge ${{\text{q}}_1}$ ${{\text{F}}_{21}} = \dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}{\text{ }} \to {\text{(3)}}$
By dividing equation (2) by equation (3), we get
$
\dfrac{{{{\text{F}}_{12}}}}{{{{\text{F}}_{21}}}}=\dfrac{{\dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}}}{{\dfrac{{{\text{K}}{{\text{q}}_1}{{\text{q}}_2}}}{{{{\text{r}}^2}}}}} \\
   \Rightarrow \dfrac{{{{\text{F}}_{12}}}}{{{{\text{F}}_{21}}}} = 1 \\
 $
Clearly, the required ratio of the force on charge ${{\text{q}}_1}$ by charge ${{\text{q}}_2}$ and force on charge ${{\text{q}}_2}$ by charge ${{\text{q}}_1}$ is equal to 1

So, the correct answer is “Option C”.

Note:
It must be noted that unlike charges (those having opposite charges) attract each other in nature and like charges (those having similar type of charges i.e., either both positive or both negative) repel each other. Attraction forces on the charges act towards each other whereas repulsion forces on the charges act away from each other.