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.]

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back