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PHY2061
R. D. Field
Department of Physics
relativity_22.doc
University of Florida
Force Between Two Moving Charged Particles
Consider the force on
q
moving with velocity
v
due to
Q
moving with velocity
V
.
The moving charge Q
produces both an electric and magnetic field given by
E
V
c
B
r
r
KQ
E
×
=
−
−
=
2
2
/
3
2
2
2
2
1
ˆ
)
sin
1
(
)
1
(
θ
β
where
β
= V/c, which produce a force on
q
given by
B
v
q
E
q
F
×
+
=
and thus
)
ˆ
(
)
sin
1
(
)
1
(
ˆ
)
sin
1
(
)
1
(
2
/
3
2
2
2
2
2
2
/
3
2
2
2
2
r
V
v
r
c
KqQ
r
r
KqQ
F
×
×
−
−
+
−
−
=
Classical Result:
If is assume that v << c and V << c then we arrive at
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This note was uploaded on 10/17/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics, Charge, Force

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