Electric flux through a hemisphere due to these charge configurations

[haruspex]

Can anyone please explain me how adding a term "curved"makes problem comprehensible .

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.
Btw, I owe you an apology for confusing you. I consistently misread the text you quoted as saying that if it cuts the surface once there is NO net charge. Sorry for the noise.

 

[gracy]

When I draw for point B ,The line emerging from it also cuts the surface twice

 

[haruspex]

When I draw for point B ,The line emerging from it also cuts the surface twice
View attachment 88869

It is not possible to deduce from that drawing whether it cuts once or twice.
I interpret the diagram as meaning that the five points lie in a vertical plane bisecting the hemisphere. Consider looking at the hemisphere from point B. Some lines from there might cut the hemisphere twice, but if there are any lines that cut it only once then there will be net flux.

 

[gracy]

To cut means to pass through ,how to count how many times it (surface)gets cut?

 

[haruspex]

To cut means to pass through ,how to count how many times it (surface)gets cut?

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]

one glass surface

I don't understand this ?I mean how many surfaces are there in glass hemisphere?.

 

[haruspex]

I don't understand this ?I mean how many surfaces are there in glass hemisphere?.

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.

 

[NascentOxygen]

To cut means to pass through ,how to count how many times it (surface)gets cut?

I suggested "lots of lines" ... "in all directions". You drew just 3?

Picture the hemispherical shell as half an empty egg shell. All you have to do is to count whether each particular field line encounters hard shell once, ... or twice.

Draw lots of lines from B radiating in all directions. Where a line is "inside" the hemisphere, that portion of the line will be hidden behind the shell, so don't draw that obscured portion of any line.

 

[NascentOxygen]

To cut means to pass through ,how to count how many times it (surface)gets cut?

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]

Although I have not drawn lots of lines but I think I have found the one needed.

 

[NascentOxygen]

I think you are saying you have drawn a line that does contribute to the total flux. Can you draw on the same figure a line through the curved surface but which does not contribute net flux.

 

[gracy]

I think you are saying you have drawn a line that does contribute to the total flux

YES.

 

[gracy]

Electric field lines contributing to the electric flux originating from Charge kept at points C &D.

Right?

Can you draw on the same figure a line through the curved surface but which does not contribute net flux.

I think there can not be any line ORIGINATING from B ,C & D that cut the surface twice or more.Right?

 

[gracy]

is #post 43 correct?

 

[gracy]

Can anyone please tell me is #post 43 correct?

 

[NascentOxygen]

Electric field lines contributing to the electric flux originating from Charge kept at points C &D.
View attachment 88876
Right?

I think there can not be any line ORIGINATING from B ,C & D that cut the surface twice or more.Right?

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]

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.

But then the lines will not cut (pass through) the surface twice.

 

[haruspex]

But then the lines will not cut (pass through) the surface twice.

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.

However, this is irrelevant to the question. To answer the question for B you only have to find one line that only cuts the surface once. Whether there are also lines that cut it twice is a separate matter.

 

[NascentOxygen]

But then the lines will not cut (pass through) the surface twice.

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.

 

[Abhikamya M S]

This is an obviously late reply ( 8yrs to be specific ) but I came across the same problem and the doubt I have is a bit different. I'm wondering why it is that only a line cutting the surface once can make a net contribution to the electric flux and not a line cutting through it twice. I think I might be using the same textbook as the original poster.

 

[haruspex]

This is an obviously late reply ( 8yrs to be specific ) but I came across the same problem and the doubt I have is a bit different. I'm wondering why it is that only a line cutting the surface once can make a net contribution to the electric flux and not a line cutting through it twice. I think I might be using the same textbook as the original poster.

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]

oh thank you so much that clears my doubt I really wasn't expecting a reply to it.