9.4 Electric field near a charged conducting surface

  Electrostatics

    1.0 Introduction
    2.0 Electric charge
    3.0 Coulomb's law
    4.0 Principle of superposition
    5.0 Continuous charge distribution
    6.0 Electric field
    7.0 Electric field lines
    8.0 Insulators and conductors
    9.0 Gauss's law
    10.0 Work done
    11.0 Electric potential energy
    12.0 Electric Potential
    13.0 Electric dipole

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9.4 Electric field near a charged conducting surface

Consider a charge is given to a conducting plate, it distributes itself over the entire outer surface of the plate. It has uniform surface charge density $\sigma $ (charge per unit area) and is same on both surfaces if the plate is of uniform thickness and of infinite size.

For calculating the electric field, we will draw the gaussian surface in the form of a cylinder as shown in the figure.

As the cylinder has three surfaces. One is curved surface and the other two are plane-parallel surface. Electric field lines at the curved surface are tangential. So, the flux passing through the curved surface is zero.

At the plane surface, the electric field has same magnitude and perpendicular to the surface. Thus from gauss law we can write, $$ES = \frac{{{q_{in}}}}{{{\varepsilon _0}}}$$
where,

$S=S_0:$ Surface area perpendicular to the field
${q_{in}} = \sigma S_0:$ Charge enclosed within the gaussian surface
$$E{S_0} = \frac{{\sigma {S_0}}}{{{\varepsilon _0}}}$$$$E = \frac{\sigma }{{{\varepsilon _0}}}$$
Thus, the electric field due to charged conducting plate is twice the field due to plane sheet of charge.