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88. The particle with charge –
q
has both potential and kinetic energy, and both of these
change when the radius of the orbit is changed. We first find an expression for the total
energy in terms of the orbit radius
r. Q
provides the centripetal force required for –
q
to
move in uniform circular motion. The magnitude of the force is
F = Qq
/4
πε
0
r
2
. The
acceleration of –
q
is
v
2
/
r
, where
v
is its speed. Newton’s second law yields
2
2
2
00
,
44
q
Q
mv
Qq
mv
rr
r
π
επε
=⇒=
and the kinetic energy is
2
0
1
28
Qq
Km
v
r
πε
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Charge, Energy, Force, Kinetic Energy

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