Electric potential, hollow metalic cylinder

AI Thread Summary
The discussion focuses on the electric potential variation along the z-axis of a hollow metallic cylinder subjected to a uniform electric field. It is established that the potential inside the cylinder remains constant at V0, despite the cylinder not being closed. The boundary conditions indicate that the potential at the cylinder's surface is V0, while the potentials at either end are V1 and V2, leading to a gradient defined by the electric field E. The conversation highlights the contradiction in assuming V1 and V2 equal V0, as it implies E equals zero, which is a trivial scenario. The participants also reference Faraday's principle regarding electric fields and shielding, noting that the field can penetrate the hollow space.
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A hollow metalic cylinder of radius r and length l, has potential V0 over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin. The cylinder is placed paralel(the electric field parallel with z axis) to an otherwise uniform electric field E.
I need the variation of electric potential V with z axis.
 
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The potential inside such a cavity would be a constant V_0.
 
Why are you saying that it's constant V_0? The cylinder is not closed as far as I understand. It's like a toilet paper roll. If it were closed with lids, I'd see why, but in this case how would you explain?

The boundary conditions are V_0 on the roll, and V_1 in one side, and V_2 in the other, such that (V_2-V_1)/l = E. If V_1 = V_2 = V_0 as you say, this means that E = 0, which is the trivial case.
 
This is not perfectly valid, because it depends on the permitivity of the cylinder. According to Faraday a metall would shield away every electric field. But if you plot the field, you will see, that the field gets into the hollow space.
 

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