Which of the following statements correctly explains/explain the existence of a positive force between two electric charges?

1. Both the charges are positive.

2. Both the charges are negative.

3. Both the charges are oppositely charged.

Select the correct answer using the code given below.

CONCEPT:

• Coulomb's law in Electrostatics: It state’s that force of interaction between two stationary point charges is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them and acts along the straight line joining the two charges.

⇒ F ∝ q1 × q2

\(⇒ F \propto \;\frac{1}{{{r^2}}}\)

\(⇒ F = K\frac{{{q_1}\; \times \;{q_2}}}{{{r^2}}}\)

Where \(K = \frac{1}{4\pi \epsilon_o}\)constant is called electrostatic force constant.

• The value of K depends on the nature of the medium between the two charges and the system of units chosen

EXPLANATION:

Case 1:

Let the magnitude of the first charge (q₁) = + q and magnitude of the second charge (q2) = -q

• The force between two charges will be

\(⇒ F' = K\frac{{{q_1}\; \times \;{q_2}}}{{{r^2}}} = K\frac{{{-q}\; \times \;{q}}}{{{r^2}}}=-F\)

• Here the force between the charges is negative which means the force is attractive in nature. 

Case 2:

Let the magnitude of the first charge (q1) = + q and magnitude of the second charge (q2) = +q

• The force between two charges will be

\(⇒ F' = K\frac{{{q_1}\; \times \;{q_2}}}{{{r^2}}} = K\frac{{{q}\; \times \;{q}}}{{{r^2}}}=F\)

• Here the force between the charges is positive which means the force is repulsive in nature. 

Case 3:

Let the magnitude of the first charge (q1) = - q and the magnitude of the second charge (q2) = -q

• The force between two charges will be

\(⇒ F' = K\frac{{{q_1}\; \times \;{q_2}}}{{{r^2}}} = K\frac{{{-q}\; \times \;{-q}}}{{{r^2}}}=F\)

• Here the force between the charges is positive which means the force is repulsive in nature. 
• Therefore, the existence of a positive force between two electric charges can be explained when both the charges are positive or negative. Hence option 3 is correct.