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PHY2061
R. D. Field
Department of Physics
relativity_14.doc
University of Florida
Electric Field of a Moving Charge Particle
Consider a point charge Q at rest at the
origin in the
O'frame
and consider the
electric field
in the
Oframe
at the moment
the origins of the two frames coincide (t = t'
= 0).
We know that,
r
r
KQ
E
′
′
=
′
ˆ
)
(
2
!
.
In the
O'frame
:
2
/
3
2
2
2
2
/
3
2
2
2
)
(
sin
)
(
)
(
cos
)
(
y
x
y
KQ
r
KQ
E
y
x
x
KQ
r
KQ
E
y
x
′
+
′
′
=
′
′
=
′
′
+
′
′
=
′
′
=
′
θ
2
2
/
sin
/
cos
y
x
r
r
y
r
x
′
+
′
=
′
′
′
=
′
′
′
=
′
In the
Oframe
:
2
2
/
sin
/
cos
y
x
r
r
y
r
x
+
=
=
=
2
1
/
1
/
β
γ
−
=
=
c
V
2
/
3
2
2
2
2
2
/
3
2
2
2
2
/
3
2
2
2
/
3
2
2
2
2
2
/
3
2
2
2
2
/
3
2
2
)
sin
1
(
sin
)
1
(
)
(
)
(
)
sin
1
(
cos
)
1
(
)
(
)
(
−
−
=
+
=
′
+
′
′
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 Spring '08
 FRY
 Physics, Charge

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