At the centre of a spherical continuous charge distribution with no external electric fields, the electric field is zero from symmetry arguments. But does the stress at the centre remain finite?
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The electromagnetic stress would still be zero, yes, because you can calculate it from $$\sigma_{i j} \equiv \epsilon_0 \left(E_i E_j - \frac{1}{2} \delta_{ij} E^2\right) + \frac{1}{\mu_0} \left(B_i B_j - \frac{1}{2} \delta_{ij} B^2\right)$$ At a point where $\vec{E} = 0$, and given that this is an electrostatic situation so $\vec{B} = 0$, all components of the stress tensor will be zero. Quantities which might not be zero would be those which involve integrals of the electric field, for example. (Also the mechanical pressure - the diagonal components of the mechanical stress tensor - would be nonzero in practice, but I'm guessing that's not what you are asking about.) |
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