Electrostatics Question 511

Question: Charges 4Q, q and Q and placed along x-axis at positions $ x=0,x=l/2 $ and $ x=l $ , respectively. Find the value of q so that force on charge Q is zero [DPMT 2005]

Options:

A) Q

B) Q / 2

C) -q / 2

D) -q

Show Answer

Answer:

Correct Answer: D

Solution:

The total force on Q $ \frac{Qq}{4\pi {\varepsilon _{0}}{{( \frac{l}{2} )}^{2}}}+\frac{4Q^{2}}{4\pi {\varepsilon _{0}}l^{2}}=0 $

$ \frac{Qq}{4\pi {\varepsilon _{0}}{{( \frac{l}{4} )}^{2}}}=-\frac{4Q^{2}}{4\pi {\varepsilon _{0}}l^{2}}\Rightarrow q=-Q. $



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