Electric potential, hollow metalic cylinder

[ale17]

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.

 

[Meir Achuz]

The potential inside such a cavity would be a constant V_0.

 

[Termotanque]

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.

 

[D'Alembert]

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.

 

[sardar]

I can provide a response to the content regarding the electric potential of a hollow metallic cylinder placed parallel to a uniform electric field. The variation of electric potential, V, with respect to the z-axis can be determined by using the formula V = V0 + Ez, where V0 is the potential over the surface of the cylinder and Ez is the contribution of the uniform electric field along the z-axis.

Since the cylinder is centered at the origin and the axis coincides with the z-axis, the potential will be constant along the entire length of the cylinder. This means that the potential at any point on the z-axis will be equal to V0, as there is no change in potential along the length of the cylinder.

However, when we introduce the uniform electric field, the potential will start to vary along the z-axis. The electric field will cause a change in potential, with the potential increasing as we move in the direction of the electric field and decreasing as we move opposite to the electric field. This can be seen in the formula V = V0 + Ez, where the potential is directly proportional to the electric field strength, E, and the distance along the z-axis, z.

In summary, the variation of electric potential, V, with the z-axis for a hollow metallic cylinder placed parallel to a uniform electric field can be represented by the equation V = V0 + Ez, where V0 is the potential over the surface of the cylinder and Ez is the contribution of the uniform electric field along the z-axis.