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An infinite nonconducting sheet has a surface charge density σ=0.10μC/m2 on one side. How far apart are equipotential surfaces whose potentials differ by 50V?
A. 8.8mm
B. 8.8cm
C. 8.8m
D. 8.8μm

Answer
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Hint: Potential of a charge conducting field is the product of the electric field and the distance between the parallel plates of the charged conductors. And the electric field on an infinite sheet is the ratio of its charge density to the relative permittivity.

Formula Used: V=Ed
Where,
V= Potential
E= Electric field
d is the separation between the plates of the charged conductor

E=σ2ε0
Where,
E is electric field due to infinite sheet
σ is the surface charge density
ε0 is the relative permittivity of free space

Complete step by step answer:Observe the diagram
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We know that, for an infinite charged sheet
E=σ2ε0
and V=Ed
where,
E is electric field
ε0=8.85×1012C2N1m2 is the permittivity of free space
σ is surface charge density of the sheet
V is potential
d is separation between the sheets
Substituting the value of E into the equation of V we get
V=σd2ε0
By rearranging it, we get
d=2Vε0σ
It is given to us that,
σ=0.10μC/m2
σ=0.10×106C/m2
σ=107C/m2
V=50V
Substituting these values in the above equation, we get
d=2×50×8.85×1012107
by simplifying it we get
d=100×8.85×105
=8.85×103m
d=0.88mm
Therefore from the above explanation the correct option is (B) 8.8cm

Note:Any surface over which the potential is constant is called an equipotential surface. In other words, the potential difference between any two points to an equipotential surface is zero. For this question, we considered the relativity of free space and it was not mentioned that there is any dielectric between the plates. But it is not always necessary. Sometimes, you might have a dielectric between the plates. Then the formula of electric field will be
E=σ2ε
Where, ε is the permittivity of dielectric.