Question

If \( f \) and \( g \) are the solutions of Laplace equation then \( \nabla \cdot \{(f \nabla g) - (g \nabla f)\ = \)}

• A. \( \nabla g \)
• B. \( 0 \)
• C. \( 1 \)
• D. \( \nabla f \)

Hint:

This expression is the integrand used in Green's Second Identity: \( \int_V (f\nabla^2 g - g\nabla^2 f) dV = \oint_S (f\nabla g - g\nabla f) \cdot d\mathbf{\hat{n}} \). Since both functions satisfy Laplace's equation, both sides of the identity are identically zero.

Answer 1

The Correct Option is B