Question

Two charges $Q$ & $-Q$ are kept at some distance, electric field at mid point is $\overrightarrow{E}$, find force on $Q$. (charges are isolated)

• A. $\frac{Q\overrightarrow{E}}{2}$
• B. $\frac{Q\overrightarrow{E}}{4}$
• C. $4Q\overrightarrow{E}$
• D. $\frac{Q\overrightarrow{E}}{8}$

Answer 1

The correct option is D $\frac{Q\overrightarrow{E}}{8}$

The electric field at the midpoint,
$\overrightarrow{E}={\overrightarrow{E}}_{+}+{\overrightarrow{E}}_{-}$
$=2{\overrightarrow{E}}_{+}$
${\overrightarrow{E}}_{+}=\frac{\overrightarrow{E}}{2}=\frac{4kQ}{r^2}$
At mid point: field due to $-Q$ is $\frac{\overrightarrow{E}}{2}$
${\overrightarrow{E}}_{+}={\overrightarrow{E}}_{-}=\frac{\overrightarrow{E}}{2}$
At position $Q$, the field is ${\overrightarrow{E}}_Q=\frac{kQ}{r^2}=\frac{\overrightarrow{E}}{8}$
Therefore the force on charge $Q$ is$\overrightarrow{F}=\frac{Q\overrightarrow{E}}{8}$