Understanding the Equation ε=ΔV/r: Parallel Plates vs. Point Charges

[BlueCardBird]

For the equation ε=ΔV/r, does this work only between 2 parallel plates or would it work for point charges as well?

 

[CWatters]

http://en.wikipedia.org/wiki/Electric_potential#Electric_potential_due_to_a_point_charge

 

[Xidike]

I love Electrostatics <3

 

[Khashishi]

Do you know calculus? Your equation seems to be another way of writing $|E| = \Delta V/\Delta r$, which is only an approximation. The correct value is gotten by taking the limit as Delta goes to 0. Then you get:
$E=-\nabla V$
In the special case of infinite parallel plate, they give the same answer, but for a curved E field you get a more accurate answer for smaller step size.

 

[sardar]

The equation ε=ΔV/r can be used for both parallel plates and point charges. The epsilon (ε) represents the permittivity of the medium, which is a constant value for a given material. The change in potential (ΔV) is the difference in electric potential between two points, and the distance (r) is the distance between those two points. This equation is a general expression for the electric field between two points, regardless of whether they are parallel plates or point charges.

In the case of parallel plates, the electric field is constant between the plates and is given by ε=ΔV/d, where d is the distance between the plates. This is a special case of the general equation, where the distance (r) is equal to the distance between the plates (d).

For point charges, the electric field is given by ε=q/4πε₀r², where q is the charge of the point and ε₀ is the permittivity of free space. This is also a special case of the general equation, where the distance (r) is equal to the distance between the two charges.

Therefore, the equation ε=ΔV/r can be applied to both parallel plates and point charges, as long as the appropriate values for permittivity and distance are used. It is a versatile equation that can be used to calculate the electric field in a variety of situations.