Question 26.9: If Φ = 2x² −y² −z², find ∇Φ, ∇ · (∇Φ) and deduce that Φ sati......
If Φ = 2x² −y² −z², find ∇Φ, ∇ · (∇Φ) and deduce that Φ satisfies Laplace’s equation.
Step-by-Step
\begin{array}{l}{{\nabla\phi=4x\mathbf{i}-2y\mathbf{j}-2z\mathbf{k}}}\\ {{\nabla .(\nabla\phi)=4-2-2=0}}\end{array}
that is,
\nabla^{2}\phi=0Hence Φ satisfies Laplace’s equation.
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