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June 8th, 2014, 08:53 PM   #1
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vector field, divergence, curl

hi,
for vector field;

V=(e^x) i + sin(y^2) j + cos(z^5) k.

im trying to find the;
a) divergence
b) divergence at a particular point, P.
c) curl
d) curl at a particular point, P.

i have worked through it but am not sure if i have done it correctly. see attached.

thanks
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June 9th, 2014, 07:54 PM   #2
jks
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Hi harley05,

a), c) and d) look correct, but b) does not.

$\cos{\sqrt{\pi/2}^2}=\cos{\pi/2}=0$ and you used 0.5. Did you mistake it for $\cos{\pi/3}$? Also, $\sin{\sqrt[5]{\pi}^5}=\sin{\pi}=0$ and you used 0.0548. I think for this one your calculator was calculating in degrees instead of radians.
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June 9th, 2014, 09:27 PM   #3
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thanks, was calculating in degrees.

So is the divergence & curl vector or scalar quantity?

With a curl = 0 what does this say about the vector field?
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June 10th, 2014, 10:16 AM   #4
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Hi harley05,

Divergence is a scalar, curl is a vector.

If the curl of a vector field is 0 everywhere then the field is conservative.
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