Question

Two point charge $Q$ and $-3Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $\overrightarrow{E}$, the field at the location of $-3Q$ is:

• A. $\overrightarrow{E}$
• B. $-\overrightarrow{E}$
• C. $+\frac{\overrightarrow{E}}{3}$
• D. $-\frac{\overrightarrow{E}}{3}$

Answer 1

The correct option is C $+\frac{\overrightarrow{E}}{3}$

Given Electric field at $A=\overrightarrow{E}$

$\overrightarrow{E}$ : Magnitude & direction

Magnitude : $E$

direction : $(x-axis)$

Now, $E=\frac{K\left(3Q\right)}{r^2}$ {Electric field due to charge at $B$}

or $\frac{KQ}{r^2}=E^1$ {$E^1:$ Electric field magnitude at $B$ due to $A$}

$\therefore E^1=\frac{E}{3}$

for direction at $E^1$, $\therefore$ $Q$ is a +ve charge particle & electric field will be along $+x-axis$,

$\therefore \overrightarrow{E}=+\frac{\overrightarrow{E}}{3}$ {or in direction of $\overrightarrow{E}$ itself}

$\therefore$ Option (C) is the correct answer.