Question

Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of +60 pC/m2, and the other carries a charge density of –80 pC/m2. What is the magnitude of the electric field at any point not on either surface?

Answer 1

The electric field at any point not on either surface is 11.28 N/C.

Step-by-step explanation:

Given that,

The surface charge density of first sheet,
`\sigma_1=+60\ pC/m^2=60* 10^(-12)C/m^2`

The surface charge density of second sheet,
`\sigma_2=-80\ pC/m^2=-80* 10^(-12)C/m^2`

The relation between the electric field and the surface charge density is given by :

`E=(\sigma)/(\epsilon_o)`

For first sheet :

`E_1=(\sigma_1)/(\epsilon_o)\\\\E_1=(60* 10^(-12))/(8.85* 10^(-12))\\\\E_1=6.77\ N/C`

For second sheet,

`E_2=(\sigma_2)/(\epsilon_o)\\\\E_2=(-80* 10^(-12))/(8.85* 10^(-12))\\\\E_2=-9.03\ N/C`

The net magnitude of the electric field at any point not on either surface is given by :

`E=√(E_1^2+E_2^2) \\\\E=√((6.77)^2+(-9.03)^2) \\\\E=11.28\ N/C`

So, the electric field at any point not on either surface is 11.28 N/C.