Phys 106 First Midterm Examination
Page 1
Saturday, 16July, 2011
PROBLEM (1)
(25 points)
A rod of length
L
carries uniformly distributed positive total
charge
Q
and it lies along the
x
axis, as shown in the figure.
A charged particle with positive charge
Q
is located at the
point
x
= 0,
y
=
r
. Express your answers in terms of
L
,
Q
,
r
,
k
e
and unit vectors
.
(a) (10 pts) Find the electric field
!
E
1
due to the rod at a point
P
that is located along the axis of the rod and a distance
r
from one end.
Q
L
r
P
r
x
y
Divide the rod into small segments of charge
dq
.
P
x
x
dx
dq
dE
E
1
=
dE
=
k
e
"
"
dq
x
2
=
k
e
#
dx
x
2
where
#
=
Q
L
r
r
+
L
"
E
1
=
k
e
Q
L
dx
x
2
r
r
+
L
"
=
k
e
Q
L
#
1
x
$
%
&
'
(
)
r
r
+
L
E
1
=
k
e
Q
L
1
r
"
1
r
+
L
#
$
%
&
'
(
=
k
e
Q
r
(
r
+
L
)
!
E
1
=
k
e
Q
r
(
r
+
L
)
(
"
"
i
)
(b) (5 pts) Find the electric field
!
E
2
at the point
P
due to the charged particle.
E
2
=
k
e
Q
r
2
!
E
2
=
k
e
Q
r
2
(
"
"
j
)
(c) (5 pts) Find the resultant field
!
E
at the point
P
.
!
E
=
!
E
1
+
!
E
2
=
k
e
Q
r
(
r
+
L
)
(
"
"
i
)
+
k
e
Q
r
2
(
"
"
j
)
!
E
=
k
e
Q
1
r
(
r
+
L
)
(
"
"
i
)
+
1
r
2
(
"
"
j
)
#
$
%
&
'
(
(d) (5 pts) An electron with mass
m
and charge –
e
is located at
P
and released from rest. Ignore any gravitational effects and
find the electron's acceleration
a
just after it is released. Express your answer in terms of the given quantities and constants,
including
m
and
e
, as needed.
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 Spring '11
 NoProfessor
 Physics, Charge, Electrostatics, Magnetic Field, Electric charge

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