| Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason: |
| (R). Mark the correct choice as: |
| Assertion (A): For charge to be in equilibrium, sum of the forces on charge due to rest of the two charges must be zero. |
| Reason (R): A charge is lying at the centre of 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) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
C) Assertion (A) is true but Reason (R) is false
D) Assertion (A) is false and Reason (R) is also false
Correct Answer: C
Solution :
(c) According to Coulomb's law, \[F=k\frac{{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}\] The force on q due to A \[{{F}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Qq}{{{\left( r/2 \right)}^{2}}}\](to the right) Due to B, \[{{F}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Qq}{{{\left( r/2 \right)}^{2}}}\](to the right) \[\therefore \]Their sum is zero whether q is \[+\frac{Q}{4}\]or \[-\frac{Q}{4}\]or any other value. Therefore, it is not true that the third charge has to be Q/4 only. It can be any value.
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