question_answer

Charges 4Q, q and Q and placed along x-axis at positions \[x=0,\text{ }x=1/2\]and\[x=1\]respectively. Find the value of q so, that force on charge Q is zero

A)  Q               

B)  \[Q/2\]

C)  \[-Q/2\]           

D)  \[-Q\]

Correct Answer: C

Solution :

 The total force on Q \[\frac{Qq}{4\pi {{\varepsilon }_{0}}{{\left( \frac{1}{2} \right)}^{2}}}+\frac{4{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}{{l}^{2}}}=0\] \[\Rightarrow \] \[\frac{Qp}{4\pi {{\varepsilon }_{0}}{{\left( \frac{1}{2} \right)}^{2}}}=-\frac{4{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}{{l}^{2}}}\] \[\Rightarrow \] \[q=-Q\]