Question

Two uniform infinite sheets with electric charge densities Ï and âÏ intersect at a right angle. Find the direction of the electric field everywhere.

Answer 1

Here we know that two infinite charge sheets are arranged perpendicular to each other

Here electric field due to infinite charge sheet is always perpendicular to the sheet

and the electric field is given by the formula

$E = \frac{\sigma}{2\epsilon_0}$

now we know that both sheets are charged with same magnitude of charge density but the sign of charge is different here

so here we can say that electric field at common point due to each sheet will have perpendicular field but one plate will exert field lines outwards while other plate will exert inwards field

so here direction of net electric field will be given as

$tan\theta = \frac{E_y}{E_x}$

here we know that

$E_y = E_x =\frac{\sigma}{2\epsilon_0}$

so we have

$tan\theta = 1$

[tex]\theta = 45 degree[\tex]

so field will make 45 degree angle