4) Charges
Q
,
Q
, and
q
lie on the corners of an equilateral
triangle with sides of length
a
.
(a) What is the force on the charge
q
?
(b) What must q be for
E
to be zero halfway up the altitude
at P?
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5) Find the electric field along the zaxis
due to four point charges q placed along
the vertices of a square with side of length
a in the xy plane centered at the origin
when:
(a) the charges have the same polarity,
q
1
=
q
2
=
q
3
=
q
4
=
q
(b) the charges alternate in same polarity,
q
1
=
q
3
=
q
q
2
=
q
4
=
−
q
(c) the charges are
q
1
=
q
2
=
q
q
3
=
q
4
=
−
q
6) Find the total charge in each of the following distributions where a is a constant parameter:
(a) An infinitely long line charge with density:
λ
z
( )
=
λ
0
e
−
z
/
a
(b) A spherically symmetric volume charge distributed over all space
ρ
r
( )
=
ρ
0
1
+
r a
(
)
−
4
(c) An infinite sheet of surface charge with density
σ
x
,
y
(
)
=
σ
0
e
−
x
/
a
1
+
y b
(
)
−
2
7) An infinitely long hollow semicylinder of radius R carries a uniform surface charge
distribution
σ
0
.
(a) What is the electric field along the axis of the cylinder?
(b) Use the results of (a) to find the electric field along the axis due to a semicylinder of
volume charge density
ρ
0
.
(c) Repeat (a) and (b) to find the electric field at the center of a uniformly surface or volume
charged hemisphere.
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 Summer '13
 BenjaminYellen
 Charge, Electric charge, Fundamental physics concepts, charge density

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