
An infinite nonconducting sheet has a surface charge density on one side. How far apart are equipotential surfaces whose potentials differ by ?
A.
B.
C.
D.
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:
Where,
Potential
Electric field
is the separation between the plates of the charged conductor
Where,
is electric field due to infinite sheet
is the surface charge density
is the relative permittivity of free space
Complete step by step answer:Observe the diagram
We know that, for an infinite charged sheet
and
where,
is electric field
is the permittivity of free space
is surface charge density of the sheet
is potential
is separation between the sheets
Substituting the value of into the equation of we get
By rearranging it, we get
It is given to us that,
Substituting these values in the above equation, we get
by simplifying it we get
Therefore from the above explanation the correct option is (B)
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
Where, is the permittivity of dielectric.
Formula Used:
Where,
Where,
Complete step by step answer:Observe the diagram

We know that, for an infinite charged sheet
and
where,
Substituting the value of
By rearranging it, we get
It is given to us that,
Substituting these values in the above equation, we get
by simplifying it we get
Therefore from the above explanation the correct option is (B)
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
Where,
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