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The variation of electric field strength and electric potential for a hollow conductor

You can show by experiment that there is no charge inside a hollow charged conductor - all the charge is on the surface. This means that the electric field inside the sphere is also zero and the potential is constant. The variation of electric field intensity and the electric potential for a hollow charged conductor is shown in the following graphs.

Example problem
The graph shows the variation of potential around a point charge in a vacuum.
Use the graph to calculate:
(a) the electric field intensity at d = 24 nm
(b) the size of the charge

Assume (1/4πε_o) = 9x10⁹ Fm^-1
(a) gradient of curve = 200/5x10^-9 = 4x10¹⁰ Vm^-1
(b) At d = 24 nm, V = 603 V therefore using V_E = (1/4πε_o)Q/d Q = V_Ed/(1/4πε_o) = 1.6x10^-15 C

Breakdown field strength for an insulator

There will come a point where the insulating properties of an insulator break down if the potential difference across it and hence the electric field strength within it is large enough. This is called the
breakdown field strength.
The value of the breakdown field strength for dry air is in the region of 5x10⁵ Vm^-
1.

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