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I am rather new to electromagnetism but I am dying.

Suppose there is a line of uniform negative charges placed at the middle of a cylinder with uniform distribution of charges on its surface, as shown below:

enter image description here

Then consider the space between the cylinder and the line, could there be any non-zero electric field?

If the charges are static and enclosed in a confined spaces, the electric field within must be 0. You may then ask, are the charges confined? If both the cylinder and the line are infinitely long, isn't that just same as being confined? Because there is no way the charge could escape the continuous, infinitely big and long space. And if you do a birdview on the system, it just looks like a cross-section of a hollow sphere containing charges fixed at the centre of the sphere, and I learnt that for such system the electric field within is indeed zero (resembles Faraday cage).

But it is too difficult to believe, by placing a charge between a positive and a negative charge, the first charge won't move. Could someone enlighten me, please?

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There is a radial field inside the cylinder. There is no component of the field along the axis of the cylinder. So the charges are in equilibrium even if the wire and the cylinder were conductors. You did not mention if the cylinder is conductor or insulator but the field will be the same in both cases (for infinite cylinder). The confinement part is not relevant.

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