Electromagnetism - Surface Charge Density

A point charge –q coulombs is placed at a distance d from a large grounded conducting plane. The surface charge density on the plane a distance D from the point charge is

A. q/4πD
B. (qD²)/2π
C. qd/(2πD²)
D. qd/(2πD³)
E. qd/(4πϵ₀D²)

(GR8677 #63)

Solution:

dq = σdA

The unit for surface charge density  σ = coulomb/meter²

A. q/4πD → unit = coulomb/meter → FALSE
B. (qD²)/2π → unit = coulomb meter² → FALSE
C. qd/(2πD²) →unit = coulomb/meter → FALSE
D. qd/(2πD³) → unit = coulomb/meter² → TRUE
E. qd/(4πϵ₀D²) → unit = coulomb/meter → FALSE

Answer: D

Note: click HERE for complete calculation.