 1 
1.
A square with each side of length
L
has four charges fixed in place at
each
corner.
At two of the corners we have a negative charge – Q, while a
third
corner has a positive charge twice as large (+ 2Q).
In the final corner
there
is a different charge
q
.
(i) Find the magnitude of the net force on charge
q
.
(ii) The total force on the +2Q charge is zero.
What must
q
be for this to be true?
2.
Two very small spheres, each of mass
m
, are suspended from a common point by
insulating threads of length
L
.
When each sphere carries a charge
q
, the threads each
make an angle of q with the vertical.
(Note: assume the radius of each sphere is
negligible relative to
L
.)
(i) By drawing a clear freebody diagram for one of the spheres, show that the string
tension in either thread is
θ
=
cos
mg
F
T
Drawing the free body diagram for the right sphere
The yequation for equilibrium is
0
mg

cos
F
T
=
θ
Rearrange to get
θ
=
cos
mg
F
T
(ii) Show that the magnitude of the charge
q
is given by
k
mg
L
q
θ
θ
=
tan
sin
2
.
The xequation for equilibrium is
0
sin
)
sin
(2L
q
2
2
=
θ
−
θ
T
F
k
Rearrange to get
k
mg
L
q
θ
θ
=
tan
sin
2
– Q
– Q
+2 Q
q
L
F
1
=
2
L
Q
q
k
(+
y
ˆ
)
F
2
=
2
L
Q
q
k
(+
x
ˆ
)
F
3
=
2
L)
2
(
(2Q)
q
k
(

2
2
x
ˆ

2
2
y
ˆ
)
F
NET
=
2
L
Q
q
k
(1 
2
2
)
(
x
ˆ
+
y
ˆ
)
F
NET 2Q
=
2
2
L
Q
2
k
(
x
ˆ

y
ˆ
) +
2
2L
2Q
q
k
(
+
2
2
x
ˆ
+
2
2
y
ˆ
)
just set the
(
x
ˆ
)
part to zero (the
(
y
ˆ
)
equation is identical)
2
2
L
2Q
k
=
2
2L
Q
q
2
k
2
2
q = Q
2
4
= Q 2
2
θ
F
T
F
E
m g
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
 2 
3.
Two equal charges +
Q
are at two vertices of an equilateral triangle
with
sides a; a third charge –
q
is at the other vertex.
A fourth charge
q
0
,
located at
a
/2 outside the triangle along the bisector of the +
Q
charges
(as
shown) experiences zero net force.
Find the ratio
Q
q
Assume the charge q
0
is positive.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Giese
 Charge, Work, Electric charge, 1.0 M, 1.0 g, 10 M, 2 mg, 11 M

Click to edit the document details