Special Relativity - Electric Field

The infinity xy-plane is a nonconducting surface, with surface charge density σ, as measured by an observer at rest on the surface. A second observer moves with velocity v relative to the surface, at height h above it. Which of the following expressions gives the electric measured by this second observer?

A.

B.

C.

D.

E. 

(GR9677 #49)

Solution:

E_z = γE_0z 
with γ = 1/(1 − ^v2/_c²)^½ 

E_z = E₀/(1 − ^v2/_c²)^½

For infinity plane: E = σ/2ɛ₀ (show)

For infinity xy-plane: E₀  = σ / 2ɛ₀

E_z =  σ / 2ɛ₀(1 − ^v2/_c²)^½

Answer: C

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.

Electromagnetism - Method of Image

A positive charge Q is located at a distance L above an infinite grounded conducting plane, as shown in the figure above. What is the total charge induced on the plane?

A. 2Q
B. Q
C. 0
D. –Q
E. –2Q

(GR0177 #08)

Solution:

Method of image:

• +Q attracts negative charges in the plate and repels positive ones. 
• As the positive charges want to “get away”, they succeed in doing so through the ground, leaving the negative charges behind. 
• The plate is left with a net negative charge.

Answer: D