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No lecture this Wednesday, Feb. 2.
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Exam 1 on Feb 15 (Tuesday), 8-9:30 PM,
1

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E
of Uniformly Charged Thin Rod
In vector form:
E
y
0
1
4
0
Q
r
r
2
L
/ 2
2
ˆ
r
At center plane
Check the results:
Direction
Units
Special case
r
>>
L:
E
y
0
1
4
0
Q
r
2
ˆ
r
Special case 2:
L
>>
r
(very long rod)
1
2
Q
/
L
ˆ
E
y
0
4
0
r
r
1/
r
dependence!
Q
/
L
– linear charge density
2

E
of Uniformly Charged Rod
At distance
r
from midpoint along
a line perpendicular to the rod:
E
0
1
Q
ˆ
r
y
4
0
r
r
2
L
/ 2
2
F
l
d
For very long rod:
E
1
4
2
Q
/
L
ˆ
r
0
r
Field at the ends:
Numerical calculation
3

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General Procedure for Calculating Electric
Field of Distributed Charges
1.
Cut the charge distribution into pieces for which the field is known
2.
Write an expression for the electric field due to one piece
(i)
Choose origin
(ii) Write an expression for
Δ
E
and its components
3.
Add up the contributions of all the pieces
(i)
Try to integrate symbolically
(ii) If impossible – integrate numerically
4.
Check the results:
(i)
Direction
(ii)
Units
(iii) Special cases
4