question_answer

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]

A)            Q   

B)            Q / 2

C)            ? Q / 2

D)                                      ? Q

Correct Answer: D

Solution :

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