PH-212
La Rosa
Example
The figure shows a “semi-infinite” nonconducting rod (that is, infinite in one
direction only) has uniform linear charge density . Show that the electric field E
at point P makes an angle of 45o with the rod. Notice that this result of 45o
orientation is independent of the distance R.
(Hint: Separately find i) the component of E parallel to the rod, and ii) the
component of E perpendicular to the rod.
+ + + + +
+
+
+
+
+
+
R
P
Answer
q


The total electric field at
P is the sum of the
individual fields
produced by the
different charges q
located along the rod.
q
q
R
Y
P
X
dEx , dEy )
Let’s choose a generic charge q located at the coordinate “s’ along the rod.
s
Electric field produced
by the charge q
(located at the
coordinate “s”) at the
point P
R

q

Y
P
d E = ( dEx , dEy )
X
Notice, the Ex and Ey components are equal.
Hence, the electric filed makes 45o with the rod; this happens for any value of R
that we choose.
__________________________
Example (To be compared with the previous example)
The figure below shows nonconducting rod in the form of a circular quadrant of
+ +P. Evaluate
+ + + the
+ electric
+ + filed
+ at P.
radius “R” with center at +
the+point
R
P
Notice, the Ex and Ey components are equal.
Hence, the electric filed makes 45o with the horizontal axis.
Example Comparing the electric fields produced by a semi-infinite line and a
quadrat.
Credit to former student Mr. Rong Wu ( PH-212, Summer 2006), who brought this
comparison to my attention.
R
In the graph above,  is the linear charge density.
Show that (2) and (3) are equal.
__________________