A potential field is expressed as V = 5r^2 volts in free space. Determine: (a) E; (b) D; (c) Calculate the amount of flux coming out of a hemisphere of radius r = 2 m, 0.002T.
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The gradient of V is given by: ∇V = (∂V/∂x)i + (∂V/∂y)j + (∂V/∂z)k Since V = 5r^2, where r is the distance from the origin, we can express V in terms of Cartesian coordinates as: V = 5(x^2 + y^2 + z^2) Taking the partial derivatives, we get: ∂V/∂x = 10x ∂V/∂y Show more…
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