question_answer

Point charge \[{{q}_{1}}=2\mu C\] and \[{{q}_{2}}=-1\,\mu C\] are kept at points \[x=0\] and \[x=6\] respectively. Electrical potential will be zero at points                                                                [MP PMT 2004]

A)            \[x=2\] and \[x=9\]

B)                                      \[x=1\] and \[x=5\]

C)                    \[x=4\] and \[x=12\] 

D)            \[x=-2\] and \[x=2\]

Correct Answer: C

Solution :

             Potential will be zero at two points At internal point (M) :\[\frac{1}{4\pi {{\varepsilon }_{0}}}\times \left[ \frac{2\times {{10}^{-6}}}{(6-l)}+\frac{(-1\times {{10}^{-6}})}{l} \right]=0\] Þ l = 2 So distance of M from origin; x = 6 ? 2 = 4 At exterior point (N) :\[\frac{1}{4\pi {{\varepsilon }_{0}}}\times \left[ \frac{2\times {{10}^{-6}}}{(6-l')}+\frac{(-1\times {{10}^{-6}})}{{{l}^{'}}} \right]=0\] Þ \[l'=6\] So distance of N from origin, x = 6 + 6 = 12