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63. First, we need a formula for the field due to the arc.
We use the notation
λ
for the
charge density,
λ
=
Q
/L
.
Sample Problem 223 illustrates the simplest approach to
circular arc field problems. Following the steps leading to Eq. 2221, we see that the
general result (for arcs that subtend angle
θ
) is
[]
arc
00
2s
i
n
(/
2
)
sin( / 2) sin(
/ 2)
44
E
rr
λ
λθ
θθ
πε
=−
−
=
.
Now, the arc length is
L = r
θ
with
θ
is expressed in radians.
Thus, using
R
instead of
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 Fall '10
 HY
 Charge

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