| ASSERTION: For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero. |
| REASON: A charge is lying at the center of the line joining two similar charges each which are fixed. The system will be in equilibrium if that charge is one fourth of the similar charges. |
A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true and reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
E) If assertion is false but reason is true.
Correct Answer: C
Solution :
According to Coulomb's law, \[F=k\frac{{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}\] The force on q due to A. \[{{F}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{Q}_{1}}q}{{{\left( r/2 \right)}^{2}}}\]to the right. Due to B. \[{{F}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Qq}{{{\left( r/2 \right)}^{2}}}\]to the left. \[\therefore \]Their sum is zero whether q is \[+\frac{Q}{4}\]or \[-\frac{Q}{4}\] or any other value. Therefore, it is not true that third charge has to be \[\frac{Q}{4}\]only. It can be any value.
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