Solution Found!
Gradient fields Find the gradient field F = ??for the
Chapter 14, Problem 31E(choose chapter or problem)
QUESTION:
Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).
\(\varphi(x, y, z)=\left(x^{2}+y^{2}+z^{2}\right)^{-1 / 2}\)
Text Transcription:
varphi(x, y, z)= x^2+y^2+z^2^-1 / 2
Questions & Answers
QUESTION:
Gradient fields Find the gradient field \(\mathbf{F}=\nabla \varphi\) for the following potential functions \(\varphi\).
\(\varphi(x, y, z)=\left(x^{2}+y^{2}+z^{2}\right)^{-1 / 2}\)
Text Transcription:
varphi(x, y, z)= x^2+y^2+z^2^-1 / 2
ANSWER:Solution 31E
Step 1:
Given that
ϕ(x, y, z) = (x2 + y2 + z2)−1/2