Electric flux : hemisphere

1. Sep 18, 2015

gracy

1. The problem statement, all variables and given/known data
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."

3. 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!

Last edited by a moderator: Sep 18, 2015
2. Sep 18, 2015

haruspex

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?

3. Sep 18, 2015

gracy

Yes

4. Sep 18, 2015

gracy

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

5. Sep 18, 2015

haruspex

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.

6. Sep 18, 2015

gracy

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

7. Sep 18, 2015

haruspex

Cut is the same as pass through.

8. Sep 18, 2015

gracy

So,what's next?

9. Sep 18, 2015

gracy

post #2 is still a problem?

10. Sep 18, 2015

haruspex

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

11. Sep 18, 2015

gracy

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.

12. Sep 18, 2015

haruspex

Yes.

13. Sep 18, 2015

gracy

???

14. Sep 18, 2015

gracy

post #2 is no longer a problem?

15. Sep 18, 2015

Staff: Mentor

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.

Last edited: Sep 18, 2015
16. Sep 18, 2015

gracy

I have copied from my book without any error.

17. Sep 18, 2015

Staff: Mentor

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

18. Sep 18, 2015

gracy

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

19. Sep 18, 2015

Staff: Mentor

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

20. Sep 18, 2015

gracy

Besides crying,What else can I do ?