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PHY2061
R. D. Field
Department of Physics
curl_3.doc
Univesity of Florida
The Curl of a Radial Function
Suppose
)
,
,
(
z
y
x
F
!
is a radial (
or central
) function of r.
Namely,
r
r
f
r
F
!
!
)
(
)
(
=
,
it points radially outward (or
inward) along the radius vector
z
z
y
y
x
x
r
ˆ
ˆ
ˆ
+
+
=
!
and
has a magnitude rf(r) that depends only on the distance
2
2
2
z
y
x
r
+
+
=
from the origin.
Theorem: The curl of a radial function is zero.
0
=
×
∇
F
!
!
if
f
F
!
!
(
=
Proof:
r
f
r
f
r
f
F
!
!
!
!
!
!
!
×
∇
+
×
∇
=
×
∇
=
×
∇
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics

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