Question

By the superposition principle, the electric field due to a system of $n$ charges is

• A. $\frac{1}{4\pi {\epsilon }_0}{\sum }_{i=1}^n\frac{q_i}{r_{ip}^3}{\hat{r}}_{ip}$
• B. $\frac{1}{4\pi {\epsilon }_0}{\sum }_{i=1}^n\frac{q_i}{r_{ip}^2}{\hat{r}}_{ip}$
• C. $\frac{1}{4\pi {\epsilon }_0}{\sum }_{i=1}^n\frac{q_i}{r_{ip}^2}$
• D. $\frac{1}{4\pi {\epsilon }_0}{\sum }_{i=1}^n\frac{q_i}{r_{ip}^3}$

Answer 1

Answer: (B)

${\vec{E}}_p={\vec{E}}_1+{\vec{E}}_2+\dots +{\vec{E}}_n$
$=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1}{r_{1P}^2}{\hat{r}}_{1P}+\frac{q_2}{r_{2P}^2}{\hat{r}}_{2P}+\dots \right]=\frac{1}{4\pi {\epsilon }_0}{\sum }_{i=i}^n\frac{q_i}{r_{iP}^2}{\hat{r}}_{iP}$