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  4. Two point charges Q and -3Q are placed certain distance apart. If the electric field at the location of Q be E, then that at the location of -3Q will be :

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Q. Two point charges $Q$ and $-3Q$ are placed certain distance apart. If the electric field at the location of $Q$ be $\overrightarrow{E}$, then that at the location of $-3Q$ will be :

Electrostatic Potential and Capacitance

Solution:

Step 1: $E$ is electric field due to charge $-3 Q$ at the location of $Q$
$
E =\frac{1}{4 \pi \epsilon_{0}} \frac{3 Q }{ x ^{2}} \ldots . .(1)
$
Step 2: $E ^{\prime}$ is electric field due to charge $Q$ at the location of $-3 Q$
$
E ^{\prime}=\frac{1}{4 \pi \epsilon_{0}} \frac{ Q }{ x ^{2}} \ldots . .(2)
$
From equation (1) and (2)
$
E^{\prime}=\frac{E}{3}
$