Electrostatics Question 169
Question: Three charges $ 4q,Q $ and $ q $ are in a straight line in the position of 0, $ l/2 $ and $ l $ respectively. The resultant force on $ q $ will be zero, if $ Q= $ [CPMT 1980]
Options:
A) -q
B) $ -2q $
C) $ -\frac{q}{2} $
D) $ 4q $
Show Answer
Answer:
Correct Answer: A
Solution:
The force between 4q and q; $ F _{1}=\frac{1}{4\pi {\varepsilon _{0}}}\cdot \frac{4q\times q}{l^{2}} $
The force between Q and q; $ F _{2}=\frac{1}{4\pi {\varepsilon _{0}}}\cdot \frac{Q\times q}{{{(l/2)}^{2}}} $
We want $ F _{1}+F _{2}=0 $ or $ \frac{4q^{2}}{l^{2}}=-\frac{4Qq}{l^{2}} $
therefore $ Q=-q $
