Question

Using Gauss’s law, deduce an experession for electric field at a point due to a uniformly charged infinite plane thin sheet.

Answer 1

Gauss’s law:

`oint vec E * d vec A = Q_"enc"/epsilon_0`

Take a cylindrical “pillbox” of cross-sectional area A passing through the sheet.

By symmetry, the electric field is perpendicular to the sheet and has the same magnitude on both sides.

Flux through curved surface = 0

Flux through two flat faces:

Φ = EA + EA

= 2 EA

Charge enclosed:

Q_enc = σA

2EA = `(sigma A)/epsilon_0`

E = `sigma/(2 epsilon_0)`