How to prove that a electric field is constant

[Edwan]

I know mathematicly how to prove that a electric field is constant on an infinite plane, but how physicly I could prove that a electric field is constant ( i.e without mathematical equation) on an infinite plane, which means that the electric field don't change because of the radius like in a normal charge ( where the electric field change by 1/r².

Thank you!






P.S. Its not an homework question!

 

[Defennder]

Intuitively, you can visualise that the closer you get to the infinite plane, fewer of the direction vectors originating from the plane to the point remain orthogonal to the plane. Which means that the E-field contributions from those parts of the plane decrease, whereas the E-field contribution from the point on the plane directly underneath the point increases. The decrease from the other parts of the plane = increase due to that point on the plane directly underneath that point. So it sorts of cancels out.

Granted this is a very hand-waving type of explanation, but it's the best you can come up without working through the equations.

 

[astrokreng]

I understand your curiosity about the physical proof of a constant electric field on an infinite plane. While mathematical equations are important and reliable tools in proving the constancy of an electric field, there are also physical experiments and observations that can demonstrate this concept.

One approach to physically prove the constancy of an electric field on an infinite plane is by using a test charge. A test charge is a small object with a known electric charge that can be placed at different points on the infinite plane. By measuring the force exerted on the test charge at different points, we can determine the strength of the electric field at those points. If the electric field is truly constant, the force measured at each point should be the same.

Another way to physically demonstrate the constancy of an electric field is through the use of equipotential lines. These are imaginary lines that connect points with the same electric potential. In a constant electric field, these lines should be evenly spaced and parallel to each other, indicating a uniform electric field. This can be observed by using a voltmeter to measure the electric potential at different points on the infinite plane.

Additionally, we can use Gauss's law, which states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. By choosing a closed surface that is parallel to the infinite plane, we can calculate the electric flux and compare it to the enclosed charge. If the values are equal, it further supports the constancy of the electric field on the infinite plane.

In conclusion, while mathematical equations are important in proving the constancy of an electric field on an infinite plane, physical experiments and observations such as using a test charge, equipotential lines, and Gauss's law can also provide evidence for this concept. By combining both mathematical and physical approaches, we can confidently prove the constancy of an electric field on an infinite plane.