The discussion centers on the electric flux through a hemispherical surface due to charge configurations, specifically a charge q at the center and a second charge Q at various positions (A, B, C, D). It is established that if the electric field lines from charge Q cut the hemispherical surface once, they contribute to the net electric flux. Conversely, if the lines cut the surface twice, as is the case for positions A and E, they do not contribute to the net flux. The confusion arises from the interpretation of the terms "cut" and "pass through," which are clarified to mean the same in this context.
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The point of adding that was to make it clear that it is not a closed hemisphere, i.e. the surface does not include a flat base.gracy said:
It is not possible to deduce from that drawing whether it cuts once or twice.gracy said:
Imagine the hemisphere as made of tinted glass. If you were to look from point B, what would it look like? Are there parts where you would only be looking through one glass surface?gracy said:
I don't understand this ?I mean how many surfaces are there in glass hemisphere?.haruspex said:
If you look through a glass (tumbler, wineglass) at eye level you will look through two surfaces, one near you and one on the other side. If stand up so that you are now looking down at an angle at the glass, you will still be looking through two layers of glass in some places, but only through one layer in others.gracy said:
I suggested "lots of lines" ... "in all directions". You drew just 3?gracy said:
Imagine shooting a bullet along each field line. If the bullet makes just one hole in the curved shell, we say it cuts the shell once; if a bullet's path would leave two holes in the half egg shell, then we say that field line cuts the shell at each of those points─so it cuts twice.gracy said:
YES.NascentOxygen said:
I think there can not be any line ORIGINATING from B ,C & D that cut the surface twice or more.Right?NascentOxygen said:
Wrong. Get half an orange, and a steel skewer, and I'm sure you'll find many ways to pierce the orange so that the curved surface gets holed twice. One hole on entry, a second at its exit.gracy said:
But then the lines will not cut (pass through) the surface twice.NascentOxygen said:
Yes they will. Consider B. A line straight down will only cut the surface once. A line making a tangent to the hemisphere will not cut it at all. A line ever so slightly below the tangent will cut the hemisphere, taking it to the inside, but almost immediately cut it a second time and find itself back outside.gracy said:
Remember, "the surface" is not the solid body; the surface is just the thin shell. We are talking of a straight line intersecting the outside shell at two spots.gracy said:
Because the direction in which the line passes through matters. Consider a closed manifold. Having passed from outside it to inside it, a second crossing by the flux line must be from inside to outside. That has the opposite sign and the two cancel.Abhikamya M S said: