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)

$\frac{8\,Q}{4\pi \varepsilon _{0}d^{2}}$

Answer 2

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
$E={{E}_{1}}+{{E}_{2}}$
$=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{4Q}{{{d}^{2}}}+\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{4Q}{{{d}^{2}}}$
$=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\,\frac{8Q}{{{d}^{2}}}$