Electric Field: Find Electric Field from 2 Infinite Planes

[nns91]

Homework Statement

AN infinite plane in the xz plane carries a uniform surface charge density 65 nC/m^2. A second infinite plane carrying a uniform charge density 45 nC/m^2 intersect the xz plane at the z axis and makes an angle of 30 degree with the xz plane. Find the electric field in the xy plane at
(a) x=6m, y=2m
(b) x=6m, b=5m

Homework Equations

E=2*k*$$\pi$$*$$\sigma$$

The Attempt at a Solution

So the electric field due to the xz plane will be only in j direction (upward) so I just use the formula above to get the electric field.

Then how can I move on with the electric field due to the remaining plane ? I don't really know what do I use the position for

 

[rl.bhat]

Find E1 and E2 due to the two planes using relevant equation.
in (a) tanθ = y/x = 2/6 = 1/3. So θ < 30 degrees. Hence point lies between the planes.
In that situation what is angle between the electric fields?
Similarly see what happens in (b).

 

[nns91]

Will it be 150 degree ?

 

[rl.bhat]

Will it be 150 degree ?

Yes.

 

[nns91]

so do I use this 150 degree to calculate the component of the Electric field due to the 2nd plane ?

The electric field due to the first plane is just in y direction (upward), right ?

 

[rl.bhat]

Yes.