Question

For a system of n point charges, what is the mathematical expression for the total electric field at point P?

विकल्प

• \[E(r) = \frac{1}{4\pi\varepsilon_0}\sum_{i=1}^n q_i r_{iP}^2\hat{\mathbf{r}}_{iP}\]

• \[E(r) = \frac{1}{4\pi\varepsilon_0}\sum_{i=1}^n\frac{q_i}{r_{iP}}\hat{\mathbf{r}}_{iP}\]

• \[E(r) = \frac{1}{4\pi\varepsilon_0}\sum_{i=1}^n\frac{q_i}{r_{iP}^2}\hat{\mathbf{r}}_{iP}\]

• \[E(r) = 4\pi\varepsilon_0\sum_{i=1}^n\frac{q_i}{r_{iP}^2}\hat{\mathbf{r}}_{iP}\]

Answer 1

The formula for the total electric field due to a system of n point charges is derived by summing the individual electric field contributions from each charge. The term \[\frac{1}{4\pi\varepsilon_0}\] is Coulomb's constant, \[q_i\] is the i-th charge, \[r_{iP}^2\] is the square of the distance from the charge to point P, and \[\hat{\mathbf{r}}_{iP}\] is the unit vector pointing from the charge toward point P.