Energy Density of a Particle Moving at Uniform Speed

contourplot

electric energy density

magnetic energy density

E

z

B

z

S

z

vectorfield

xy component of electric field

xy component of magnetic field

xy component of Poynting vector

z position

10

velocity

100000000

time

0

The four components of the potential

A

μ

ϕ,

v

2

c

ϕ,0,0

of a point charge, whose position at the time

t

is

(vt,0,0)

, at the observation points

-∞<t,x,y,z<∞

are used to compute various electric and magnetic properties. The time component is the scalar potential

ϕ

and the three space components are the vector potential (

v

2

c

ϕ

, 0, 0). The system is rotationally symmetric around the

x

axis. The scalar potential for cylindrical coordinates,

ϕ(t,ρ,φ,x,v)

, is independent of

φ

. The observation plane is parametrized by

-h<x,y<+h

with

h

= 50 meters with an arbitrary

z

value. The charge enters the observation plane at time

-h/v

with

1×

8

10

m/s<v<2.99×

8

10

m/s

. At

t=0

the charge passes the origin with positive speed

v

. The charge leaves the observation plane at time

h/v

. The five independent variables are

t,x,y,z,v

. The electric and magnetic field vectors, the Poynting vector, and the energy density are displayed on the observation plane. SI (MSKA) units are used.