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Given the potential V = 25 sin θ, in free space, determine whether V satisfies Laplace’s equation.

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in Electromagnetic Theory by (188k points)
Given the potential V = 25 sin θ, in free space, determine whether V satisfies Laplace’s equation.

(a) Yes

(b) No

(c) Data sufficient

(d) Potential is not defined

The question was asked in homework.

My question is based upon Laplacian Operator topic in portion Vector Calculus of Electromagnetic Theory

1 Answer

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The correct answer is (a) Yes

Easy explanation: (Del)^2V = 0

(Del)^2V = (Del)^2(25 sin θ), which is not equal to zero. Thus the field does not satisfy Laplace equation.

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