Electric field of charged infinite line and plane

[Angelos]

Hi...

I have hopefuly simple question, which however drives me crazy...
I know how to mathematically derive that infinite line of charge has its electric field inversly proportional to the distance from it and also I know how to derive that infinite plane of charge has its electric field constant. Nevertheless I don't see why is this. Why the E-field of infinite line changes, but one of infinite plane does not? I mean I don't see the physical reason for it.

Thanks for any help.

 

[rbj]

i wrote a response to a similar question regarding the inverse-square law. take a look at:

https://www.physicsforums.com/showthread.php?t=188661

for, what seems to me to be, the intuitive reply. remember all this is because we live in 3 spatial dimensions.

 

[astrokreng]

I can understand your confusion about the electric field of a charged infinite line and plane. Let me explain the physical reason behind these mathematical derivations.

First, let's consider the electric field of an infinite line of charge. This line of charge has an infinite length, which means that it has an infinite number of charges. When we calculate the electric field at a point near the line, we are essentially summing up the contributions of all these infinite number of charges. As we move away from the line, the distance between the point and the charges increases, and thus the electric field decreases inversely proportional to the distance. This is because the electric field follows the inverse square law, which states that the strength of the electric field is inversely proportional to the square of the distance from the charge.

On the other hand, an infinite plane of charge has an infinite surface area, but not an infinite number of charges. The electric field at a point near the plane is determined by the charges present on that particular area of the plane. Unlike the infinite line, the distance between the point and the charges remains the same, regardless of the distance from the plane. This is why the electric field of an infinite plane remains constant, as the number of charges contributing to the field does not change with distance.

In conclusion, the physical reason behind the different behavior of electric fields for an infinite line and plane is due to the infinite length and surface area, respectively, of these charged objects. I hope this helps to clarify your confusion. Keep questioning and exploring, that's what drives scientific progress!