Unformatted text preview: 5. The electric ﬁeld produced by an inﬁnite sheet of charge has magnitude E = σ/2ε0 , where σ is 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 x axis to be parallel to the ﬁeld and positive in the direction of the ﬁeld. Then the electric potential is
x V = Vs −
0 E dx = Vs − Ex , where Vs is 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 ∆x then their potentials diﬀer in magnitude by ∆V = E ∆x = (σ/2ε0 )∆x. Thus, ∆x = 2 8.85 × 10−12 C2 /N · m2 (50 V) 2 ε0 ∆ V = 8.8 × 10−3 m . = 2 σ 0.10 × 10−6 C/m ...
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