June 8th, 2014, 08:53 PM  #1 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32  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 
June 9th, 2014, 07:54 PM  #2 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 635 Thanks: 96 Math Focus: Electrical Engineering Applications 
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. 
June 9th, 2014, 09:27 PM  #3 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32 
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? 
June 10th, 2014, 10:16 AM  #4 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 635 Thanks: 96 Math Focus: Electrical Engineering Applications 
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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curl, divergence, field, vector, vector field 
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