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. $\frac{8Q}{4\pi {\epsilon }_0{d}^2}$
• C. $\frac{6Q}{4\pi {\epsilon }_0{d}^2}$
• D. $\frac{4Q}{4\pi {\epsilon }_0{d}^2}$

Answer 1

Answer: (B)

Two equal and opposite charges are placed at a distance d.
Electric field at centre due to
$+Q$ charge $(E_1)=\frac{1}{4\pi {\epsilon }_0}\frac{(Q)}{{(d/2)}^2}$
Similarly, electric field due to $-Q$ charge $(E_2)=\frac{1}{4\pi {\epsilon }_0}\frac{(Q)}{{(d/2)}^2}$
Therefore, net electric field at point
$E=E_1+E_2$
$=\frac{1}{4\pi {\epsilon }_0}\frac{4Q}{d^2}+\frac{1}{4\pi {\epsilon }_0}\frac{4Q}{d^2}$
$=\frac{1}{4\pi {\epsilon }_0}\frac{8Q}{d^2}$