व्हाट इज द फिजिकल साइनिफिकेंस आफ डायवर्जेंस एंड कर्ल
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Consider a ball in your hand. Now take any point on the ball and imagine a vector acting perpendicular to the ball on that point. That is your gradient in 3D. Now imagine vectors acting on all points of the ball. It would look something like this:
The red arrows perpendicular to the surface of the ball are the gradients (in 3D) of various points on the ball. If we apply gradient function to a 2D structure, the gradients will be tangential to the surface.
For a better understanding of gradient representation in 2D, consider that you are climbing a mountain. You are a certain point on the mountain:
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