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4. The fact that the spheres are identical allows us to conclude that when two spheres are
in contact, they share equal charge. Therefore, when a charged sphere (
q
) touches an
uncharged one, they will (fairly quickly) each attain half that charge (
q
/2). We start with
spheres 1 and 2 each having charge
q
and experiencing a mutual repulsive force
22
/
Fk
qr
=
. When the neutral sphere 3 touches sphere 1, sphere 1’s charge decreases to
q
/2. Then sphere 3 (now carrying charge
q
/2) is brought into contact with sphere 2, a total
amount of
q
/2 +
q
becomes shared equally between them. Therefore, the charge of sphere
3 is 3
q
/4 in the final situation. The repulsive force between spheres 1 and 2 is finally
2
( / 2)(3 / 4)
3
3
'
3
0.375.
88
8
qq
q
F
k
F
rr
F
′
==
=
⇒
=
=
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View Full Document18. (a) For the net force to be in the +
x
direction, the
y
components of the individual
forces must cancel. The angle of the force exerted by the
q
1
= 40
µ
C charge on
3
20
qC
=
is 45°, and the angle of force exerted on
q
3
by
Q
is at –
θ
where
1
2.0 cm
tan
33.7 .
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 Spring '09
 Mobius
 Charge, Magnetism

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