A Geiger counter has a metal cylinder 2.10 cm in diameter along whose axis is stretched a wire in diameter. A potential difference of is applied between them. We have to find (a) the electric field at the surface of the wire; (b) at the surface of the cylinder.

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We will use Gauss’ law to find the expression for the electric field inside the Geiger counter. Let be the charge per unit length on the inner wire. Because of cylindrical symmetry electric field will be perpendicular to the axis of the cylinder. We consider a cylindrical Gaussian surface of radius r centred at the axis of the Geiger counter. By applying Gauss’ law, we have

,

or

.

Let be the radius of the wire and be the radius of the metallic cylinder of the Geiger counter. The potential difference across the Geiger counter will be

Therefore,

.

Electric field at the surface of the wire will be

Electric field at the metallic cylinder of the Geiger counter will be