Electric Charges and Fields - Result Question 6

6. A charge ’ $q$ ’ is placed at the centre of the line joining two equal charges ’ $Q$ ‘. The system of the three charges will be in equilibrium if ’ $q$ ’ is equal to

[NEET Kar. 2013, 1995]

(a) $Q / 2$

(b) $-Q / 4$

(c) $Q / 4$

(d) $-Q / 2$

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Answer:

Correct Answer: 6. (b)

Solution:

  1. (b) The system of three charges will be in equilibrium.

For this, force between charge at $A$ and $B+$ force between charge at point $O$ and either at $A$ or $B$ is zero.

i.e., $\frac{K Q^{2}}{(2 r)^{2}}+\frac{K Q q}{(r)^{2}}=0$

By solving we get,

$q=-\frac{Q}{4}$.