Does this curl operator equal 1?

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SUMMARY

The discussion centers on the application of the curl operator in electromagnetism, specifically regarding the vector field defined as V(y, 2x, 0). The user correctly identifies that the curl of this vector field results in (0, 0, 1), which corresponds to the unit vector in the z-direction, denoted as ##\hat{k}##. It is emphasized that the curl operator produces a vector, making it incorrect to equate its output to a scalar value like 1. Instead, the output can be expressed in terms of unit vectors.

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leroile
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Hello,
I am a beginner in electromagnetism.
I am trying to find a vector field whose rotation equals 1 with a curl operator. If I say that the vector field is defined by V(y;2x;0) does it work? As a result, I find (0;0;1), am I right?
 
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The curl operator returns a vector, not a scalar, so it doesn't make sense to say that it "equals 1" since 1 is just a number. You can make it equal to anyone of the following though: ##\hat{i},\hat{j},\hat{k}##. In the case of your vector, the curl returns ##\hat{k}##.
 

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