(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let the dipole [itex]\vec{m}[/itex] = m[itex]\hat{k}[/itex] be at the origin, and call a certain horizontal axis the y axis.

a) On the z axis, what is the angle between the z axis and the magnetic field?

b) On the y axis, what is the angle between the z axis and the magnetic field?

c) On the cone θ=45 degrees, what is the angle between the z axis and the magnetic field?

d) What is the angle of the cone on which the magnetic field is horizontal?

2. Relevant equations

I believe there is some relevance to the equation: [itex]\vec{B}[/itex] =[itex]\frac{μ_{0}m}{4∏r^3}[/itex](2cosθ[itex]\hat{r}[/itex]+sinθ[itex]\hat{θ}[/itex])

3. The attempt at a solution

I tried putting the previous equation into the coordinate free form to try if that would help.

[itex]\vec{B}[/itex] =[itex]\frac{μ_{0}}{4∏r^3}[/itex][3([itex]\vec{m}[/itex][itex]\bullet\hat{r}[/itex])[itex]\hat{r}[/itex]-[itex]\vec{m}[/itex]]

I then simplified this to:

[itex]\vec{B}[/itex] =[itex]\frac{μ_{0}}{4∏r^3}[/itex]m[3cosθ-1][itex]\hat{k}[/itex]

I was not sure what to do after this so I tried:

r^2=x^2+y^2+z^2

set x=0 so it's in the yz plane,

r=(y^2+z^2)^(1/2)

arccos(z/r)=θ

arccos[itex]\frac{z}{(y^2+z^2)^(1/2)}[/itex] = θ

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# Homework Help: Introduction to electrodynamics - help with a dipole problem

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