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Physics 213
HW #2 – Solutions
Spring 2008
21.59.
[EField Lines & Particle Paths]
IDENTIFY:
The force on the particle at any point is always tangent to the electric field line at that point.
SET UP:
The instantaneous velocity determines the path of the particle.
EXECUTE:
In Fig.21.29a the field lines are straight, so the force, (and therefore acceleration and velocity) are always in a straight
line in that same direction. The particle moves along the straight field line with increasing speed. In Fig.21.29b the field lines are
curved. As the particle moves, its acceleration changes direction due to the changing direction of the electric field and therefore force.
The particle’s velocity and acceleration are not in the same direction, and its trajectory does not follow a field line.
EVALUATE:
In twodimensional motion the velocity is always tangent to the trajectory but the velocity is not always in the direction
of the net force on the particle. A gravitational analog: one body in a circular orbit around another has its velocity always
perpendicular to acceleration, and a trajectory always perpendicular to the (gravitational) field line.
21.61.
[Infinite Line Charge EField Lines]
(a) IDENTIFY
and
SET UP:
The only distinguishable direction is toward
the line or away from the line, so the electric field lines are perpendicular
to the line of charge:
(b) EXECUTE
and
EVALUATE:
Consider a circle of radius
r
with the line of charge passing through the center. The spacing of field
lines, which represents the magnitude of E, is the same all around the circle. For a different r the spacing would change, so the
magnitude of E clearly depends on r. A smaller r would result in a closer spacing, which corresponds to larger E,
so E is inversely proportional r. In the direction
perpendicular
to the plane of the circle the lines are equally
spaced, so
E
does not depend on the position along the line, but rather
only
on the distance
r
. The total number of
field lines passing out through the circle is independent of the radius of the circle, so the spacing of the field lines
is proportional to the reciprocal of the circumference (2
±
r) of the circle. Hence
E
is proportional to 1/
r
.
21.89.
[Finite Line of Charge]
IDENTIFY:
Divide the charge distribution into infinitesimal segments of
length dx. Calculate
E
x
due to a segment and integrate to find the total field.
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 Spring '07
 PERELSTEIN,M
 Magnetism, Force, Heat

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