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Physics 2213
HW #2 – Solutions
Spring 2010
21.57
[Two charge sheets]
From equation 21.12 in the text, for a
uniformly charged infinite sheet, the
electric field is
0
2
ε
σ
=
E
.
Note that this
is independent of the distance from the
sheet.
Then —
Point a:
0
2
2
0
0
=
−
=
−
=
−
+
E
E
E
.
Point b:
0
=
E
, as for point a.
Point c:
0
=
+
=
−
+
E
E
E
, downward.
21.59. [EField Lines & Particle Paths]
Electric field lines are constructed so that the tangent to the field line at any point gives the
direction of the net electric field at that point.
The electric force is proportional to the electric
field, so the force vector (on a positive charge) will point along a field line.
Since acceleration is
proportional to the force (Newton's 2nd Law), the acceleration vector will also point along the
tangent to the electric field line.
(a)
In Fig.21.29a, the field lines are
straight lines
, so the force is always directed straight line away
from the charge, and the velocity and acceleration are always in the same direction.
The particle
moves in a straight line along a field line, with increasing speed.
(b)
In Fig.21.29b, the field lines are
curved
.
Suppose the charged particle followed the path of one of
these curved field lines.
In order for the particle to follow a curved path, its acceleration must
have a component perpendicular to the path (radial or "centripetal" acceleration).
This is not
possible if the particle follows a field line, since the electric field (and acceleration) must be
tangent to the field line.
As the particle moves, its velocity and acceleration are not in the same
direction, so the trajectory does not follow a field line.
21.61. [Infinite Line Charge EField Lines]
(a)
Use
symmetry
to deduce the nature of the field
lines.
The only distinguishable direction is toward or
away from the line, so the electric field lines are perpendicular to the line of charge.
(b)
The main difference between the electric field of a point charge and the electric field of a
charged line is that the field lines from a point charge spread out in 3D (in 2 angular directions),
while the field lines from a line of charge spread out in only 2D (in just 1 angular direction around
the line).
The magnitude of the electric field is inversely proportional to the spacing of the field lines,
so spreading out in fewer directions means the field falls off more slowly with distance.
+
+
+
+
+
+
+
+
+
+
+
−
− − − − −
− − − −
− −
E
+
E
−
a
c
b
E
+
E
−
E
+
E
−
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To see how this spacing between field lines changes with
r
, the distance from the line,
imagine that the line of charge is surrounded by a
cylinder
of radius
r
and length L
centered on the charged line.
The diagram shows the view looking along the line and
cylinder axis.
The field lines spread out with distance r in the directions around the line,
but they maintain constant spacing in the direction along the line or the cylinder's axis. The number of
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 Spring '08
 PERELSTEIN
 Charge

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