Physics · JEE | Electric Charges and Fields

What is the expression for the electric field at position vector \( \mathbf{r} \) due to a system of discrete charges \( q_1, q_2, \dots, q_n \) located at position vectors \( \mathbf{r}_1, \mathbf{r}_2, \dots, \mathbf{r}_n \)?

1. A
   \( \mathbf{E}(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i=1}^{n} \frac{q_i}{r_{iP}} \hat{\mathbf{r}}_{iP} \)
2. B
   \( \mathbf{E}(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i=1}^{n} \frac{q_i}{r_{iP}^2} \hat{\mathbf{r}}_{iP} \)
3. C
   \( \mathbf{E}(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i=1}^{n} \frac{q_i^2}{r_{iP}^2} \hat{\mathbf{r}}_{iP} \)
4. D
   \( \mathbf{E}(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i=1}^{n} \frac{q_i}{r_{iP}^3} \hat{\mathbf{r}}_{iP} \)