Using the method of images, a point charge q at distance d from an infinite grounded conducting plane experiences what force magnitude and direction?

Using the method of images, a point charge q at distance d from an infinite grounded conducting plane experiences what force magnitude and direction?

• A. F = (1/(4π ε0)) q^2 /(d^2) directed away from the plane.
• B. F = (1/(4π ε0)) q^2 /(4 d^2) directed toward the plane (attractive).
• C. F = (1/(4π ε0)) q^2 /(8 d^2) directed toward the plane.
• D. F = (1/(4π ε0)) q^2 /(2 d^2) directed toward the plane.

Answer: (B)

Think of the grounded plane as replaced by an image charge of equal magnitude but opposite sign located symmetrically on the other side. The real charge sits a distance d from the plane, and the image charge sits the same distance on the opposite side, so the separation between the two charges is 2d. The force on the real charge is the Coulomb force due to the image: F = (1/4πε0) q^2 / (2d)^2 = (1/4πε0) q^2 / (4 d^2). Since the image has opposite sign, the interaction is attractive, pulling the real charge toward the plane. The force is perpendicular to the plane, toward it.

Think of the grounded plane as replaced by an image charge of equal magnitude but opposite sign located symmetrically on the other side. The real charge sits a distance d from the plane, and the image charge sits the same distance on the opposite side, so the separation between the two charges is 2d. The force on the real charge is the Coulomb force due to the image: F = (1/4πε0) q^2 / (2d)^2 = (1/4πε0) q^2 / (4 d^2). Since the image has opposite sign, the interaction is attractive, pulling the real charge toward the plane. The force is perpendicular to the plane, toward it.