DylanG
Oct18-10, 09:15 PM
1. The problem statement, all variables and given/known data
Consider a magnet floating over a large piece of superconductor. Treat
the magnet as a perfect dipole m floating a distance h from the surface
of the superconductor, which we take to be the x–y plane. The dipole is
oriented at an angle of θ to the z-axis, and without loss of generality we
take it to lie in the y–z plane (m_x = 0).
(a) First, derive an expression for the magnetic field at the surface of the
superconductor due to the dipole.
Hint: start with the expression for the field of a dipole m positioned
at the origin.
Bdip(r) = (μ0/(4πr3))(3(m·\hat{r})\hat{r}-m)
3. The attempt at a solution
I started with r = (0,0,-h) , m·\hat{r} = mcosθ, m = (0, -msinθ, -mcosθ)
After evaluating I got,
B = (μ0m/(4πh3))(0,sinθ,-2cosθ)
I suspect that this is incorrect however as I really can't get my head around the coordinate system. I tried to draw it but I don't even really know what the dipole is supposed to look like or where things are positioned relative to the origin in the coordinate system.
Consider a magnet floating over a large piece of superconductor. Treat
the magnet as a perfect dipole m floating a distance h from the surface
of the superconductor, which we take to be the x–y plane. The dipole is
oriented at an angle of θ to the z-axis, and without loss of generality we
take it to lie in the y–z plane (m_x = 0).
(a) First, derive an expression for the magnetic field at the surface of the
superconductor due to the dipole.
Hint: start with the expression for the field of a dipole m positioned
at the origin.
Bdip(r) = (μ0/(4πr3))(3(m·\hat{r})\hat{r}-m)
3. The attempt at a solution
I started with r = (0,0,-h) , m·\hat{r} = mcosθ, m = (0, -msinθ, -mcosθ)
After evaluating I got,
B = (μ0m/(4πh3))(0,sinθ,-2cosθ)
I suspect that this is incorrect however as I really can't get my head around the coordinate system. I tried to draw it but I don't even really know what the dipole is supposed to look like or where things are positioned relative to the origin in the coordinate system.