# Magnetic flux through a disk

1. Nov 2, 2008

### Monocles

1. The problem statement, all variables and given/known data
Consider a thin disk normal to the z-axis, of thickness dz and radius p centered on the axis of a dipole.

a. Show that

$$0 = \oint \vec{B} \cdot d\vec{A} \approx (2\pi p dz)B_{r} + (\pi p^{2}) a (dB_{z} / dz)$$, so $$B_{p} \approx (-p/2)(dB_{z} / dz)$$

b. With B_z for a dipole, find B_p near the axis (small p).

2. Relevant equations

$$0 = \oint \vec{B} \cdot d\vec{A}$$

3. The attempt at a solution
I don't know where to start because the book doesn't bother to define B_r, B_z, B_p, or a. Is there some standard definition for these? I thought it might be partial derivatives, but this is an intro physics class and we have yet to use partial derivatives anywhere and the book went over the math needed to do things.