Three nonconducting infinite sheets are parallel to the y z plane of an x y z co

Question

Three nonconducting infinite sheets are parallel to the yz plane of an xyz coordinate system. Each sheet has a uniform surface charge density. Sheet 1, negatively charged with surface charge density p, passes through the x axis at x=1.0 = 1.0 m . Sheet 2 has an unknown surface charge density and passes through the x axis at x = 2.0 m . Sheet 3, negatively charged with surface charge density 3p, and passes through the xaxis at x = 4.0 m . The electric field due to the sheets is zero at x = 1.5 m .

A)

What is the surface charge density on sheet 2?

Express your answer in terms of p.

B)

If the electric field at x = 0 is E0?, what is the electric field magnitude at x = -2.0 m ? What is it at x = 3.0 m and x = 6.0 m ?

Express your answer in terms of the variable p and the permittivity constant e0.

Explanation / Answer

PART A -- For x = -1 cm, I summed the two individual electric fields. For the sheet I said the electric field would be positive since the sheet's charge is negative so the field lines are going in the positive x direction (towards the sheet). For the slab I said the electric field was negative since the slab had positive charge, so the field lines are going away from the slab (i.e. in the negative x direction) -- For x = 1 cm, same logic. I summed both individual fields again. This time both were negative since field lines for both the sheet and the slab were headed in the negative x direction. -- For x = 2.5 cm, the electric field is zero since it is within the conductor and conductors have zero electric fields within them. -- For x = 6 cm, I only used the electric field of the slab, since I thought it would block the field of the sheet. However I said it had a sigma of 2

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