Download Physics Lecture #23

Tue. Jan. 27 – Physics Lecture #23
Electric Field, Continued (and Continuous!)
1. Electric Field due to Continuous Charge Distributions
Warm-up:
Consider a very thin rod, length 2L, that has a total
charge Q uniformly distributed along its length and is
oriented as shown.
P
How can we determine the electric field at the point P?
Brainstorm with your neighbors and come up with
some strategies.
-L
L
ConceptCheck: Consider the very thin rod, length
2L with a total charge Q uniformly distributed along
its length as shown.
P
What is the direction of the electric field at the
point P?
1. No field
2. Down
3. Up
4. Right
5. Left
6. Not enough information
-L
L
P
(0, yP)
dQ
-L
(x, 0)
L
A line of charge, length 2L, with uniform linear charge density l = Q/2L is
oriented along the x-axis as shown. A field point P is on the y-axis at the point
(0, yP). The electric field at the point P is given by
P
L
dx
E y  ky P l  2
2 3/ 2
( x  yP )
L
2kl

yP
L
L y
2
2
P
-L
L
Consider the case where yP is very large compared to L or alternatively where
the field point is very far away from the line charge. What is a good
approximation for Ey?
Consider the case where L is very large compared to yP, or alternatively where
the field point is very close to the line charge. What is a good approximation for
Ey?
Example: Consider the semicircular arc shown in the figure,
with radius a. The arc has charge uniformly distributed along
its length with uniform linear charge density l. Set up the
integral that will allow you to calculate the x-component of
the electric field at the origin, due to this charge distribution.

k
d
y
a

x