The electric field from an infinitely large and uniform sheet is independent of
ID: 1618312 • Letter: T
Question
The electric field from an infinitely large and uniform sheet is independent of the distance from the sheet, yet the individual charges in the sheet all produce fields that object the inverse square law. Why doesn't he field get weaker at great distances? The electric field from an infinitely large and uniform sheet is independent of the distance from the sheet, yet the individual charges in the sheet all produce fields that object the inverse square law. Why doesn't he field get weaker at great distances?Explanation / Answer
Since the sheet is infinitely large, any distance you choose whether 1 m from the sheet or 10,000 km from the sheet - both these distances are equivalent as seen by the sheet of charge because its own dimensions are infinite.
It's like trying to find the difference in heat experienced by an object by putting it 100 m from the surface of the sun and then 1 km from the surface of the sun. Both these distances will experience almost equivalent heat and that's when the dimensions and heat released by the sun is negligible compared to infinitely large dimensions any hypothetical sun can have.
Same is the situation with the infinite sheet of charge.
Suppose a sheet of charge has very large dimensions, say, billions of kilometers long and wide. This cannot be termed as infinite sheet. Now consider a distance of 1 m and 10 m from this large sheet. If you calculate the field, the difference at two points will be negligible. And this difference will keep getting smaller if you keep making the sheet larger and larger and the difference will become zero once the sheet has infinite dimensions.
Same is the case for difference in field for any two points when we have sheet of infinite dimensions.
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