# Volume distribution of charge

1. Feb 13, 2010

### Ripperbat

1. The problem statement, all variables and given/known data

A rod of dielectric material is spun about it's axis with angular velocity $$\omega$$. A uniform magnetic field B exists in a direction along the axis of the bar. Determine a charge distribution which produces the same electric field as does the rotating rod. The electric susceptibility of the material is xE

2. Relevant equations

3. The attempt at a solution

The force on a charge q at a distance r is F=q*$$\omega$$*r*B and the electric field is E=r*B*$$\omega$$.
The polarization of the rod at distance r is P=xE*$$\epsilon$$0*$$\omega$$*B*r.
So the volume distribution of charge should be -div P = -($$\partial$$Pr) / ($$\partial$$*r). But according to the book it should be
-div P = -($$\partial$$Pr) / ($$\partial$$*r) - (Pr) / r .

Could somebody please explain why it should be that way?? thx

2. Feb 14, 2010

### Redbelly98

Staff Emeritus
That is the divergence in cylindrical coordinates.

http://hyperphysics.phy-astr.gsu.edu/Hbase/diverg.html#c3

3. Feb 15, 2010

### Ripperbat

Thank you thank you thank you! :!!)