Two point charges lie on the x‑axis. A charge $q_1 = +8\,\mu\text{C}$ is at the origin and a charge $q_2 = -2\,\mu\text{C}$ is at $x = 0.12\,\text{m}$.

(a) Find the point on the perpendicular bisector of the line joining the charges at which the magnitude of the resultant electric field is a minimum. Give the coordinates of this point.
(b) Determine the electric potential difference between this point and the point $(0.20\,\text{m},0)$ on the x‑axis.
(c) A test charge of $5.0\,\mu\text{C}$ is moved quasistatically from the point found in (a) to the point $(0.20\,\text{m},0)$. Calculate the work done by the external agent in this process.

Question

Two point charges lie on the x‑axis. A charge $q_1 = +8\,\mu\text{C}$ is at the origin and a charge $q_2 = -2\,\mu\text{C}$ is at $x = 0.12\,\text{m}$.

(a) Find the point on the perpendicular bisector of the line joining the charges at which the magnitude of the resultant electric field is a minimum. Give the coordinates of this point.
(b) Determine the electric potential difference between this point and the point $(0.20\,\text{m},0)$ on the x‑axis.
(c) A test charge of $5.0\,\mu\text{C}$ is moved quasistatically from the point found in (a) to the point $(0.20\,\text{m},0)$. Calculate the work done by the external agent in this process.

Accepted Answer

(a) (0.06 m, 0); (b) ΔV = -7.6×10⁵ V; (c) work ≈ 3.8 J (positive, done by external agent)

Gce Model Questions Vol1 2022 Physics Question 17

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