Calculate Div & Curl from V=Kyi-Kxj

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SUMMARY

The discussion focuses on calculating the divergence and curl of the vector field defined as V=Kyi-Kxj. The user seeks clarification on the proper formatting of the vector field, questioning whether to express it as V{x,y}={Ky,-Kx}. It is confirmed that this reformulation leads to a divergence of zero, as both partial derivatives dV1/dx and dV2/dy equal zero. The conclusion is that the divergence of the given vector field is indeed zero.

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  • Study the mathematical definitions and properties of divergence and curl in vector calculus.
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laforzadiment
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Determine Div & Curl from a given vector field

V=Kyi-Kxj

How do I format this?

It's been a while since I've done this and every divergence and curl example I look up has the format V(x,y,z)={V1(x,y,z);V2(x,y,z);V3(x,y,z)}

Should I reformat my V to be V{x,y}={V1(x,y);V2(x,y)}={Ky,-Kx} because of the unit vectors i and j?

The Attempt at a Solution



I think the above mentioned method is the correct way of reformatting it but doing it that way means dV1/dx=0 and dV2/dy=0 so my entire divergence is 0 when summed together. Just wanted to check.
 
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You're correct. The divergence is zero.
 

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