Two infinite conducting plates 1 and 2 are separated by a distance $l = 10 ext{ cm}$. A point char

Question

Two infinite conducting plates 1 and 2 are separated by a distance $l = 10 	ext{ cm}$. A point charge $q = 5 \mu	ext{C}$ is located between the plates at a distance $x = 2 	ext{ cm}$ from plate 1. Both plates are grounded (connected to each other). Find the magnitude of the total induced charge on plate 1 (in $\mu	ext{C}$).

Professor PC Thomas Classes · Answer

For grounded parallel infinite conducting plates separated by a distance $l$, a point charge $q$ placed at a distance $x$ from plate 1 induces charges on both plates such that their sum equals $-q$. The ratio of the induced charges depends on the distances to the plates. The configuration acts like two capacitors in parallel or can be solved using the reciprocal theorem/method of images. The exact relation for the total induced charge on plate 1 is $q_1 = -q \frac{l-x}{l}$, and on plate 2 is $q_2 = -q \frac{x}{l}$. The magnitude of the induced charge on plate 1 is $|q_1| = q \frac{l-x}{l}$. Substituting the given values: $q = 5 \mu	ext{C}$, $l = 10 	ext{ cm}$, $x = 2 	ext{ cm}$. $|q_1| = 5 	imes \frac{10 - 2}{10} = 5 	imes \frac{8}{10} = 4 \mu	ext{C}$.