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Suppose we have a uniformly charged hollow cone(ice cup) of surface charge density σ, slant height L and the half-angle at the vertex is θ. I want to calculate the electric field at its tip using Gauss law. I have done the calculation using Coulomb's Law by dividing the cone into rings of thickness dx and integrating over x and I have obtained:

$$E = \sigma \frac{\sin \theta \cos \theta}{2 \epsilon_0} \int_0^L \frac{1}{x}dx$$

which diverges. Can I do the same using Gauss law?

Vaggelis Peppas
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  • What do you mean by "do the same with Gauss's Law"? Do you mean "can you show that the field diverges using Gauss's Law"? Do you mean "does Gauss's Law yield a finite value at the tip"? (BTW, the field really is infinite at the tip of an infinitely sharp cone; see Section 3.4 of Jackson's Classical Electrodynamics.) – Michael Seifert Jan 04 '24 at 18:43
  • Gauss law is only useful for what you want if you can find a surface in which the electric field is normal and has the same magnitude along the surface. It is no possible to find such possible surface here. – Pato Galmarini Jan 04 '24 at 19:14

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