Curl of a Vector Field in space, curl F
, where F
= F(x, y, z)
In general:
F(x, y, z) = P(x,y,z) i +
Q(x,y,z) j + R(x,y,z) k
i j k
curl F = det ∂/∂x ∂/∂y ∂/∂z
P Q R
where det means
determinant.
Expansion of this
determinant gives for the curl of the vector field, F(x,y,z)
curl F
= ( ∂R/∂y - ∂Q/∂z
) i
+ ( ∂P/∂z -
∂R/∂x) j +
( ∂Q/∂x - ∂P/∂y
) k
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