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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 ±eld 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 far±eld limit (but not in±nitedistance limit) approximation to the formula
for part (a).
023 qfull 00250 3 3 0 tough math: in±nite line charge
2. What is the electric ±eld (size and direction) around an in±nite line of charge with linear charge
density
λ
.
HINTS:
Divide and conquer: what is the electric ±eld at an arbitrary point in space
due to an arbitrary di²erential bit of the line? Also: by symmetry what must be the direction
of the electric ±eld? And lastly, a conversion to angular integration saves nine (of what? cat
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 Fall '06
 Buchler
 Physics, Charge

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