5. The electric field produced by an infinite sheet of charge has magnitude E=σ/2ε0,whereσis the
surface charge density. The field is normal to the sheet and is uniform. Place the origin of a coordinate
system at the sheet and take the xaxis to be parallel to the field and positive in the direction of the
field. Then the electric potential is
V=Vs−x
0
Edx=Vs−Ex ,
where Vsis the potential at the sheet. The equipotential surfaces are surfaces of constant x; that is,
they are planes that are parallel to the plane of charge. If two surfaces are separated by ∆xthen their
potentials differ in magnitude by ∆V=E∆x=(σ/2ε0)∆x.Thus,
∆x=2ε0∆V
σ=28.85 ×10−12 C2/N·m2(50 V)
0.10 ×10−6C/m2=8.8×10−3m.
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