# Electric field due to infinite sheet of charge

by jyothsna pb
Tags: charge, electric, field, infinite, sheet
 P: 675 A simple explanation: The electric field of a point charge is inversely proportional to r^2. For a line charge, it is infinite in one of the directions so you will never be far enough away from it to observe the 1/r^2, but you can observe the 1/r. You are basically replacing one of the r's with L, and then you have Q/L = $\lambda$ (charge per unit length). For a 2d sheet, it is infinite in 2 directions. So that completely cancels out the 1/r^2 and you are left with a constant. Or replacing both r's in r^2 with A = area to get $Q/A = \sigma$ (charger per unit area). This is a very basic explanation.
 P: 675 Electric field due to infinite sheet of charge Take the infinite line charge in the z-direction as an example. If you cut out an infinitesmal plane in the x-y direction, then you can solve the electric field in that plane alone with charge, $\lambda dx$. And you can say it is periodic above and below this plane to get back the full solution. So you have a 2D poisson equation for a point charge. This ends up giving you a 1/r term for the electric field. So the infinite line charge acts like a point charge in 2 dimensions. You can do the same for an infinite sheet charge in the x-y plane, by taking a 1D space in the z-direction and saying it is periodic in the x and y-directions. Solve for the E-field in 1D space, you get a constant. So an infinite sheet charge acts like a point charge in 1 dimension.