- #1
Frank Einstein
- 170
- 1
Homework Statement
I have a problem with the next situation. I have a magnetic dipole moving at constant speed on the z axis. On the plane z=0 I have a circular wire with a resistance R and radius a. I have to calculate the electromotive force on the wire as a function of the speed of the dipole, v, the position of the dipole ,z, and the dipolar moment m.
Homework Equations
ε=-dΦ/dt, where ε is the electromotive force and Φ is the magnetic flux.
B=(μ0/(4π))*(3r(r*m)/r5-m/r3)
Φ=∫Bds
ds=( cosφ, sinφ, 0)
r = (a cos φ, a sinφ, z)
The Attempt at a Solution
Once I calculate a huge expression for the magnetostatic field, B, and I integrate to find the flux, my problem comes; I have to make a time derivate, and the only time dependent factor here is z; but Φ(r(z(t))) do I have to derivate (∂Φ/∂z)(dz/dt)=(∂Φ/∂z)v or do I have to do something else?