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Forms Tour
Exterior Product The forms exterior product or wedge operator is much like the vector cross product. The exterior product of two forms creates a form of higher order. For example a dx form and and dy form wedged together make a two form (dx^dy = dz) in the z direction. Any form wedged with itself is zero. That is, dx^dx = dy^dy = dz^dz = 0. Using forms it is easier to see what certain operations represent. For example if we do the cross product of the electric field and magnetic field in vectors (E x H = S) all we get is another vector, the Poynting Vector. In forms the cross product is done with the exterior product operator. So in form when we do the E form wedged with the H form (dE ^ dH = dS) the S form is a tube through wich the power flows (this will be shown in the next animation). Why would this be more useful? |