Problem 1.19 Draw a circle in the xy plane. At a few representative points draw the vector v tangent to the circle, pointing in the clockwise direction. By comparing adjacent vectors, determine the sign of avx/ay and avy/ax. According to Eq. 1.41, then, what is the direction of V x v? Explain how this example illustrates the geo- metrical interpretation of the curl. ? From the definition of V we construct the curl: Vxv= a/ax / ŷ Ĉ /a Ux Vy Vz = ✰ ( მა- avy aux მა. avy θυχ +ŷ +2 (1.41) ду Əz Əz дх Əx ду
Problem 1.19 Draw a circle in the xy plane. At a few representative points draw the vector v tangent to the circle, pointing in the clockwise direction. By comparing adjacent vectors, determine the sign of avx/ay and avy/ax. According to Eq. 1.41, then, what is the direction of V x v? Explain how this example illustrates the geo- metrical interpretation of the curl. ? From the definition of V we construct the curl: Vxv= a/ax / ŷ Ĉ /a Ux Vy Vz = ✰ ( მა- avy aux მა. avy θυχ +ŷ +2 (1.41) ду Əz Əz дх Əx ду
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
Transcribed Image Text:Problem 1.19 Draw a circle in the xy plane. At a few representative points draw
the vector v tangent to the circle, pointing in the clockwise direction. By comparing
adjacent vectors, determine the sign of avx/ay and avy/ax. According to Eq. 1.41,
then, what is the direction of V x v? Explain how this example illustrates the geo-
metrical interpretation of the curl.

Transcribed Image Text:?
From the definition of V we construct the curl:
Vxv= a/ax /
ŷ
Ĉ
/a
Ux
Vy
Vz
= ✰
(
მა-
avy
aux
მა.
avy
θυχ
+ŷ
+2
(1.41)
ду Əz
Əz
дх
Əx
ду
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