Chapt. 23
The Electric Field
183
FullAnswer Problems
023 qfull 00240 2 5 0 moderate thinking: charge rod, integration
1. There is a thin uniformly charged rod of length
L
. The total charge is
q
. The rod’s thickness
is negligible: it can be treated as a line of charge.
a) What is the formula for the electric field a distance
x
away from one end of the rod and
along the axis of the rod?
HINTS:
Find the expression for charge per unit length and
then divide and conquer by integration. Draw a diagram.
b) What is the farfield limit (but not infinitedistance limit) approximation to the formula
for part (a).
023 qfull 00250 3 3 0 tough math: infinite line charge
2. What is the electric field (size and direction) around an infinite line of charge with linear charge
density
λ
.
HINTS:
Divide and conquer: what is the electric field at an arbitrary point in space
due to an arbitrary differential bit of the line? Also: by symmetry what must be the direction
of the electric field? And lastly, a conversion to angular integration saves nine (of what? cat
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 Fall '06
 Buchler
 Physics, Charge, Electric charge, Fundamental physics concepts

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