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### Gauss' Law in differential form applied to charged sphere

I think this problem is ill posed. The divergence operator is not generally invertible. There are many functions with the same divergence. We need further information of electric field on a region of ...
1 vote

### 2D Gauss law vs residue theorem

There is a very good discussion of this in Tristan Needham's Visual Complex Analysis final chapter, but I'd like to share one other view point of it. When we have some charge configuration or so, we ...
1 vote
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### Integrate continuity equation in QM

The integral $$\int \psi^*\psi\ r^2\ dr\ d\Omega$$ is just the same as integral $$\int P(\mathbf{r},t) d^3\mathbf{r}$$ representing the total probability of finding the particle anywhere. Remember ...
1 vote

### Why can't electric field by a single charge be at an angle?

The symmetries of the charge distribution say something about the symmetries of the resulting electric field. For example $\rho$ has rotational symmetry $\implies$ $\vec E$ only depends on $r$ $\rho$ ...
1 vote

### Why can't electric field by a single charge be at an angle?

The experimental study of electricity led to modeling the data with formulas that not only modeled the data, but were also predictive of new measurements. The attraction between two point charges . ...
1 vote

### No net charge in conductor or no charge at all? Electrostatics

Since conductors are made of atoms, which are made of particles with charge, there are still charges in conductors. There is no net charge within a conductor; any net charge resides on the surface(s).
1 vote

### Charge kept inside a conducting sphere not at its center

This is a conductor and in static equilibrium all charges are on the surfaces of the conductor, and the $\vec E$ inside the conductor is $0$. This follows because, if there’s an $\vec E$-field inside, ...

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