Question

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}}$

Answer 1

Answer: (B)

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}}} $