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?