Electric Flux Calculation for Oppositely Charged Circular Plates

[xcvxcvvc]

Homework Statement

Two circular parallel metal plates are oppositely charged with q = ±1.0 nC. The two plates each have a radius of 5.00 cm and are separated by 1.00 mm. (a) Estimate the electric flux for a circular area of radius 5.00 cm sandwiched between the two plates. (b) Repeat for a circular area of radius 5.00 meters – the result would be essentially the same. Explain why this would be the case.

I don't know how to start. I thought that any charge outside a gauss surface is zero to that surface.

 

[G01]

This isn't really a Gauss's Law problem. Gauss's Law deals with flux through closed surfaces. Here, we have an open surface.

HINT: Let's start at the beginning. Can you state the definition of electric flux for me?

 

[Moetasim]

I understand that the electric flux is a measure of the electric field passing through a given surface. In the case of oppositely charged circular plates, the electric flux can be calculated using the formula Φ = q/ε₀, where q is the total charge enclosed by the surface and ε₀ is the permittivity of free space.

In this scenario, the circular area of radius 5.00 cm is sandwiched between the two plates, with a charge of ±1.0 nC on each plate. This means that the total charge enclosed by the circular area is zero, as the positive and negative charges cancel each other out. As a result, the electric flux through this circular area is also zero.

For part (b) of the question, the circular area has a much larger radius of 5.00 meters. However, the distance between the two plates remains the same at 1.00 mm. This means that the total charge enclosed by the circular area is still zero, as the charges on the plates are relatively small compared to the distance between them. Therefore, the electric flux through this circular area would also be zero.

In summary, the electric flux through a circular area between two oppositely charged circular plates is zero, regardless of the area's size. This is because the electric field between the plates is constant and perpendicular to the plates, resulting in a net flux of zero through any surface between them.