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

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

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

Correct Answer: B

Solution :

Two equal and opposite charges are placed at a distance d. Electric field at centre  due to \[+\text{ }Q\]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 \[E={{E}_{1}}+{{E}_{2}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{4Q}{{{d}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{4Q}{{{d}^{2}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{8Q}{{{d}^{2}}}\]