Let E and H be two vectors assumed to have continuous partial derivatives (of second order...

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Let E and H be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations 1 JE VxH= Т Ән V.E = 0, V H =0, VxE: с д (1) c dt prove that E and H satisfy the equation V'v (2) where y is a generic meaning and, in particular, can represent any component of E or H. (The vectors E and H are called electric and magnetic field vectors in electromagnetic theory. Equations (1) are a special case of Maxwell's equations. The result (2) led Maxwell to the conclusion that light was an electromagnetic phenomena. The constant c is the velocity of light.] Let E and H be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations 1 JE VxH= Т Ән V.E = 0, V H =0, VxE: с д (1) c dt prove that E and H satisfy the equation V'v (2) where y is a generic meaning and, in particular, can represent any component of E or H. (The vectors E and H are called electric and magnetic field vectors in electromagnetic theory. Equations (1) are a special case of Maxwell's equations. The result (2) led Maxwell to the conclusion that light was an electromagnetic phenomena. The constant c is the velocity of light.]