Question

Parallel Plates Consider a very large conducting plate at potential V0 suspended a distance d above a very large grounded plane. Find the potential between the plates. The plates are large enough so that they may be considered to be infinite. This means that one can neglect fringing fields.

Answer 1

Answer:

$V = \frac{V_0x}{d}$

Explanation:

Since the field lines are parallel and the electric field is uniform between two parallel plates, a test charge would experience the same force of attraction or repulsion no matter where it is located in the field,

I attached an image that could help to understand the representation of the field. The formula used to calculate it is given by,

$E= -\frac{\Delta V}{x}$ (1)

If we want to consider the change in Voltage with respect to the position then it would be,

$E= -\frac{dV}{dx}$

According to the information provided, the potential is $V_0$ and there is a distance d, therefore

$E= -\frac{V_0}{d}$ (2)

Taking equation (1) we can clear V, to what we have,

$\frac{dV}{dx} = -E$

$dV = -Edx$

Integrating,

$V= - \int Edx$

Substituting (2)

$V = -\int \frac{V_0}{d} dx$

$V = \frac{V_0x}{d}$

Where x is the height from the grounded plate.