Electric flux through a hemisphere due to these charge configurations

[gracy]

Homework Statement

The figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A,B,C and D .in which position(s) of this second charge , the flux of the electric field through the hemisphere remains unchanged ?

2. Relevant Point:
My textbook says "if the vector E line from a charge cuts the surface once -there will be net contribution to the electric flux."

The Attempt at a Solution

In the following cases

Obviously from points A and E all the straight lines cut the surface twice as shown below.So if we happen to bring another charge Q at any of these two points the value of electric flux would not change because these will not contribute in it.But what about other points B,C & D?I am unable to figure out for these points.How to sketch the diagrams for these points?Any help would be greatly appreciated!

 

[haruspex]

My textbook says "if the vector E line from a charge cuts the surface once -there will be net contribution to the electric flux."

are you sure it says that? Seems exactly wrong to me. If the line passes through the surface an even number of times then there should be no net contribution, surely?

 

[gracy]

surely?

Yes

 

[gracy]

If the line passes through the surface an even number of times then there should be no net contribution

my book mentions about the case when the line touches the surface twice.

 

[haruspex]

my book mentions about the case when the line touches the surface twice.

Touches or passes through? If it touches without passing through, any number of times, that makes no contribution. Each pair of times it passes through there's no net contribution (two passes in opposite directions cancel), so any even number of passes also makes no net contribution. But for the present problem, it is just the two passes case that matters.

 

[gracy]

neither touch nor pass through, Actually the word "cut"is used.

 

[haruspex]

neither touch nor pass through, Actually the word "cut"is used.

Cut is the same as pass through.

 

[gracy]

Cut is the same as pass through.

So,what's next?

 

[gracy]

post #2 is still a problem?

 

[haruspex]

post #2 is still a problem?

Maybe. Please clarify what the book says about each case (cutting once, twice).

 

[gracy]

Please clarify what the book says about each case (cutting once, twice).

If the electric line from a charge Q cuts the surface once-it will make net contribution to the electric flux.
And then it has been written That electric field lines emerging straight from charge Q WHEN it is kept at points at points A and E cut the hemisphere twice hence do not contribute in net electric flux.

 

[haruspex]

If the electric line from a charge Q cuts the surface once-it will make net contribution to the electric flux.
And then it has been written That electric field lines emerging straight from charge Q WHEN it is kept at points at points A and E cut the hemisphere twice hence do not contribute in net electric flux.

Yes.

 

[gracy]

Yes.

?

 

[gracy]

post #2 is no longer a problem?

 

[NascentOxygen]

Gracy, please could you edit your first post in this thread and make corrections to its problem statement.

There may be some confusion in the use here of "E" to simultaneously denote the general electric field vector and also a reference point.

Your hemisphere has a curved upper surface and a flat lower surface. There is no way that field lines from any external charge can enter the hemisphere without also exiting through a surface, therefore these contribute no net flux. Only the enclosed charges can contribute flux.

EDIT. Perhaps your textbook wants you to consider only the curved surface? If you look at it that way, where there exists only the curved surface "shell", then the question makes more sense.

 

[gracy]

Gracy, please could you edit your first post in this thread and make corrections to its problem statement.

I have copied from my book without any error.

 

[NascentOxygen]

I have copied from my book without any error.

Then perhaps you could do everyone a favour and correct the textbook's blunder?

 

[gracy]

Now,how to edit?I can't see any edit option

 

[NascentOxygen]

Now,how to edit?I can't see any edit option

The editing option expires after an hour or two, so perhaps you have just missed it.

 

[gracy]

Besides crying,What else can I do ?

 

[NascentOxygen]

Besides crying,What else can I do ?

You'll have to ignore their mistake, and refocus on the problem you were asking about.

So from point B, draw lots of lines radiating outwards in all directions. Those that completely miss the hemispherical shell obviously contribute nothing to the flux through it. But what observations can you make about those field lines that don't completely miss the shell?

P.S. Your textbook is correct.

 

[gracy]

P.S. Your textbook is correct.

You'll have to ignore the mistake

Then whose mistake are we talking about?

 

[NascentOxygen]

Then whose mistake are we talking about?

There is no mistake now. There was a typing blunder in your first post, but it has now been fixed.

 

[gracy]

But I don't see word "curve"in my problem statement yet.

 

[NascentOxygen]

But I don't see word "curve"in my problem statement yet.

If you wish to improve on the textbook's clumsy problem statement, then by all means please do! Write how you think it should be in your next post and if it looks good I'll copy it to your first post.

Are you any closer to being able to answer their question, now?

 

[gracy]

But what about other points B,C & D?I am unable to figure out for these points.How to sketch the diagrams for these points?

I have drawn for Points A and E,I want help to draw the diagrams for other points B,C &D

 

[NascentOxygen]

I have drawn for Points A and E,I want help to draw the diagrams for other points B,C &D

See advice in post #21

 

[TSny]

EDIT. Perhaps your textbook wants you to consider only the curved surface? If you look at it that way, where there exists only the curved surface "shell", then the question makes more sense.

I suspect that's the intended interpretation of "hemisphere" here. Too bad they didn't make that clear in the problem statement.

 

[gracy]

Homework Statement

The figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A,B,C and D .in which position(s) of this second charge , the flux of the electric field through the hemispherical curved surface remains unchanged ?

2. Relevant Point:
My textbook says "if the vector E line from a charge cuts the surface once -there will be net contribution to the electric flux."

The Attempt at a Solution

In the following cases

Obviously from points A and E all the straight lines cut the surface twice as shown below.So if we happen to bring another charge Q at any of these two points the value of electric flux would not change because these will not contribute in it.But what about other points B,C & D?I am unable to figure out for these points.How to sketch the diagrams for these points?Any help would be greatly appreciated!

 

[gracy]

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

 

[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.