Question

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

• A. $\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=1}^{n} \frac{q_{i}}{r_{i p}^{3}} \hat{r}_{i p}$
• B. $\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=1}^{n} \frac{q_{i}}{r_{i p}^{2}} \hat{r}_{i p}$
• C. $\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=1}^{n} \frac{q_{i}}{r_{i p}^{2}}$
• D. $\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=1}^{n} \frac{q_{i}}{r_{i p}^{3}}$

Answer 1

Answer: (B)

$\vec{E}_{p}=\vec{E}_{1}+\vec{E}_{2}+\ldots+\vec{E}_{n}$
$=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q_{1}}{r_{1 P}^{2}} \hat{r}_{1 P}+\frac{q_{2}}{r_{2 P}^{2}} \hat{r}_{2 P}+\ldots\right]=\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=i}^{n} \frac{q_{i}}{r_{i P}^{2}} \hat{r}_{i P}$