Use the result of Exercise 43(b) to show that if F is a vectorfield of the form F =
Chapter 15, Problem 46(choose chapter or problem)
Use the result of Exercise 43(b) to show that if \(F\) is a vector field of the form \(F=f(\|r\|)\) and if div \(F=0\), then \(F\) is an inverse-square field. [Suggestion: Let r = || r || and multiply \(3 f(r)+r f^{\prime}(r)=0\) through by \(r^{2}\).Then write the result as a derivative of a product.]
Equation Transcription:
Text Transcription:
F
F =f(||r||)
F=0
r=||r||
3f(r) + r f’(r)= 0
r^2
Image text transcription: Use the result of Exercise 43(b) to show that if F is a vector field of the form F = f (|| r ||) and if div F = 0, then F is an inverse-square field. [Suggestion: Let r = || r || and multiply 3f(r) + r f’ ® = 0 through by r2. Then write the result as a derivative of a product.]
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