what is curl in physics
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In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the curl of that point is represented by a vector. ... A vector field whose curl is zero is called irrotational.
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In a river, water flows faster in the middle and slower near the banks of the river and hence, if I placed a twig, it would rotate and hence, the vector field has non-zero Curl. Curl{v}=∇×v But I am finding it difficult to interpret the above expression geometrically. In scalar fields, the gradient points along the direction of maximum increase. But what's the direction of gradient in a vector field? And why does the cross product give the Curl?
It is not a cross product, it simply happens to have a similar form in Cartesian coordinates. You can think of (the inner product of) the curl (with a normal to the plane) as being a measure of the line integral around a small planar loop. The direction of the curl is the direction which will maximise this line integral. This is analogous to how you may see divergence as a measure of the net flow out of the closed surface surrounding a small volume.
HOPE ITS HELP U MY FRIEND__.:-)
In a river, water flows faster in the middle and slower near the banks of the river and hence, if I placed a twig, it would rotate and hence, the vector field has non-zero Curl. Curl{v}=∇×v But I am finding it difficult to interpret the above expression geometrically. In scalar fields, the gradient points along the direction of maximum increase. But what's the direction of gradient in a vector field? And why does the cross product give the Curl?
It is not a cross product, it simply happens to have a similar form in Cartesian coordinates. You can think of (the inner product of) the curl (with a normal to the plane) as being a measure of the line integral around a small planar loop. The direction of the curl is the direction which will maximise this line integral. This is analogous to how you may see divergence as a measure of the net flow out of the closed surface surrounding a small volume.
HOPE ITS HELP U MY FRIEND__.:-)
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