- #1
fluidistic
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Homework Statement
A ring of radius R has a current density ##\vec J=J(r, \theta) \sin \phi \hat \phi## where phi is the azimuthal angle in spherical coordinates. Calculate the charge distribution considering that it was initially null.
Homework Equations
Not sure. Maybe ##\nabla \cdot \vec J + \frac{\partial \rho}{\partial t}=0##.
The divergence theorem.
The Attempt at a Solution
So my idea was to maybe use the continuity equation that I wrote above. From it, I am not sure what to do. Maybe integrate in space so that I can use the divergence theorem, in other words I can reach that ##\int _S \vec J \cdot d\vec A + \int \frac{\partial \rho}{\partial t}dV=0##. But I am stuck there because I don't know how to calculate ##\vec J \cdot d\vec A##.
Then my other idea is to integrate the continuity equation with respect to time, but again I'm not sure how to do this...
I'd appreciate a little push in the right direction, thanks!