P22_005.PDF

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Chapter 22 - 22.5
5. We put the origin of a coordinate system at the lower left corner of the square and take + x rightward
and + y upward. The force exerted by the charge + q on the charge +2 q is
F 1 = k q (2 q )
a 2
(
j) .
The force exerted by the charge
q on the +2 q charge is directed along the diagonal of the square and
has magnitude
F 2 = k q (2 q )
( a 2) 2
which becomes, upon finding its components (and using the fact that cos 45 =1 / 2),
F 2 = k
2 2 a 2 i+ k
2 2 a 2 j .
q ( 2 q )
Finally, the force exerted by the charge
2 q on +2 q is
F 3 = k (2 q )(2 q )
a 2
i .
(a)Therefore, the horizontal component of the resultant force on +2 q is
F x = F 1 x + F 2 x + F 3 x = k q 2
a 2 1
2 +4
10 9 1 . 0
10 7 2
0 . 050 2
1
2 +4 =0 . 17 N .
= 8 . 99
×
×
(b)The vertical component of the net force is
F y = F 1 y + F 2 y + F 3 y = k q 2
a 2
2+
1
2
=
0 . 046 N .
q ( 2 q )
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