question_answer

Two unlike charges of the same magnitude Q are placed at a distance d. The intensity of the electric field at the middle point in the line joining the two charges

A)  zero                                     

B) \[\frac{8Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]

C) \[\frac{6Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]                               

D) \[\frac{4Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]

Correct Answer: B

Solution :

                 Two equal and opposite charges are placed at a distance d. Electric field at centre  due to + Q charge                 \[({{E}_{1}})=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{{{(d/2)}^{2}}}\] Similarly, electric field due to -Q charge                 \[({{E}_{2}})=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{(Q)}{{{(d/2)}^{2}}}\] Therefore, net electric field at point                 \[E={{E}_{1}}+{{E}_{2}}\]                 \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{4Q}{{{d}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{4Q}{{{d}^{2}}}\]                 \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{8Q}{{{d}^{2}}}\]