- #1
BucketOfFish
- 60
- 1
A sphere has charge density [itex]\rho=k\cdot r[/itex]. Using the integral form of Gauss's Law, one easily finds that the electric field is [itex]E=\frac{k\cdot r^2}{4\epsilon}[/itex] anywhere inside the sphere. However, [itex]\nabla\cdot E=\frac{k\cdot r}{2\epsilon}[/itex], which is half of what should be expected from the differential form of Gauss's Law, since [itex]\frac{\rho}{\epsilon}=\frac{k\cdot r}{\epsilon}[/itex]. Why is this?