94. 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
Q
r
mv
r
mv
Qq
r
q
44
0
2
2
2
0
ππ
εε
=
¡
=
,
and the kinetic energy is
Km
v
Q
q
r
==
1
2
2
0
8
π
ε
. The potential energy is
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This note was uploaded on 01/25/2011 for the course PHYSICS 17029 taught by Professor Rebello,nobels during the Spring '10 term at Kansas State University.
 Spring '10
 Rebello,NobelS
 Charge, Energy, Force, Kinetic Energy

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