Which of the following option is correct by using Coulomb's law.

The correct answer is Option (4)

(if the product of \( q_1q_2 \) is negative)

By Coulomb's law the forces between two point charges act along the line joining them, and the force on \( q_1 \) due to \( q_2 \) is equal and opposite to the force on \( q_2 \) due to \( q_1 \).

    \( \displaystyle \vec{F}_{12} = -\vec{F}_{21} \)

If \( q_1q_2 \gt 0 \) (like charges) the forces are repulsive: each force points away from the other charge. If \( q_1q_2 \lt 0 \) (unlike charges) they are attractive: each force points towards the other charge.

In Option (4) the product is negative, \( \vec{F}_{12} \) on \( q_1 \) points towards \( q_2 \), and \( \vec{F}_{21} \) on \( q_2 \) points towards \( q_1 \). The two forces lie along the line joining the charges and are equal and opposite, which is the correct picture of attraction.

Why the other options are incorrect

• 

  (if the product of \( q_1q_2 \) is positive)

  Option (1) — Incorrect. For a positive product the force on \( q_1 \) correctly points away from \( q_2 \), but \( \vec{F}_{21} \) is drawn at an angle to the line joining the charges. Coulomb forces act only along that line.

• 

  (if the product of \( q_1q_2 \) is negative)

  Option (2) — Incorrect. For a negative product both forces should point towards the other charge. Here \( \vec{F}_{21} \) points away from \( q_1 \), and the two forces point the same way instead of being opposite.

• 

  (if the product of \( q_1q_2 \) is positive)

  Option (3) — Incorrect. For a positive product both forces should point away from each other. Here \( \vec{F}_{21} \) points towards \( q_1 \), and the two forces point the same way instead of being opposite.

NCERT (2026-27):
Coulomb’s Law – “… Equation (1.3) is valid for any sign of q₁ and q₂ whether positive or negative. If q₁ and q₂ are of the same sign (either both positive or both negative), \( \mathbf{F}_{21} \) is along \( \hat{\mathbf{r}}_{21} \), which denotes repulsion, as it should be for like charges. If q₁ and q₂ are of opposite signs, \( \mathbf{F}_{21} \) is along \( -\hat{\mathbf{r}}_{21} \) (\( = \hat{\mathbf{r}}_{12} \)), which denotes attraction, as expected for unlike charges.”

Coulomb’s Law – “… The force \( \mathbf{F}_{12} \) on charge q₁ due to charge q₂, is obtained from Eq. (1.3), by simply interchanging 1 and 2, i.e.,

    \( \displaystyle \mathbf{F}_{12} = -\mathbf{F}_{21} \)

Thus, Coulomb’s law agrees with the Newton’s third law.”