Derivative of Magnetic Field from a dipole

AI Thread Summary
To derive the magnetic field from a dipole with respect to r, the formula provided is B = [m/0/(4π)] * (3rhat(μ dot rhat) - μ)/|r|^3. The main confusion arises around differentiating the unit vector rhat with respect to the vector r. A suggested approach is to express rhat as (x/r, y/r, z/r) to facilitate differentiation. Understanding the relationship between rhat and r is crucial for accurately computing the derivative. This foundational knowledge will aid in completing the project effectively.
mbq
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I need to take the derivative of the magnetic field from a magnetic dipole with respect to r for a project I'm working on:

B =[m[/0]/(4π) * (3rhat(μ dot rhat) - μ)/|r|^3

where rhat is the unit vector of the vector r (or r/|r|), |r| is the magnitude of the vector r, and μ is the magnetic moment of the dipole

I'm mainly confused about how to take the derivative of rhat with respect to r

Thanks for any suggestions anyone may have!
 
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welcome to pf!

hi mbq! welcome to pf! :smile:
mbq said:
I'm mainly confused about how to take the derivative of rhat with respect to r

write ##\hat{r}## = (x/r, y/r, z/r) :wink:
 

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