Electric Field Superposition of Two Charges

← Back to Problems
Electrostatics Intermediate Electric Field

Source: High school physics (Chinese)

Problem Sets:

Electrostatics

Problem

Two point charges in air, $q_1 = +40 \, \mu$C and $q_2 = +100 \, \mu$C, are separated by 7 m. Point P lies on the line connecting the two charges, at a distance of 2 m from $q_1$. (Note: $1 \, \mu\text{C} = 10^{-6}$ C)

Find the net electric field strength at point P.
$E_P = 5.4 \times 10^4$ N/C, directed from $q_1$ towards $q_2$.

The net electric field at point P is the vector sum of the fields produced by $q_1$ and $q_2$. Let the direction from $q_1$ to $q_2$ be positive. The distance from P to $q_1$ is $r_1 = 2$ m. The distance from P to $q_2$ is $r_2 = 7 \text{ m} - 2 \text{ m} = 5$ m. The field from $q_1$ is $E_1$, directed away from $q_1$ (positive direction). The field from $q_2$ is $E_2$, directed away from $q_2$ (negative direction).

$$E_P = E_1 - E_2 = k \frac{q_1}{r_1^2} - k \frac{q_2}{r_2^2} = k \left( \frac{q_1}{r_1^2} - \frac{q_2}{r_2^2} \right)$$

A positive result means the net field is directed towards $q_2$.