# Electric field lines extending to infinity?

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1. Aug 26, 2015

### SquidgyGuff

Given a system of two charges (+7q and -q) some of the field lines will terminate at -q while others go on towards infinity. I've read that the portion of the field lines that terminate is given by (1/7), but I have no idea why that is. I am supposed to find the maxium angle of a field line leaving +7q that will still terminate.

2. Aug 26, 2015

### DEvens

Field lines either terminate on a charge, or go to infinite. Also, they either start on a charge or go to infinity. Infinity in this context is defined as "outside the concern of the experiment." So it does not really mean infinity but just very far away from the charges involved in the calculation.

So you have +7 q, meaning you have 7 units of + charge. And so you have 7 units of field lines starting from those + charges. But you have only 1 unit of - charge. So you have only 1 unit of field lines terminating on - charge.

To get the maximum angle you are going to have to make some assumptions. For example, are both charges arranged as points? Or rather, close enough to points that you can ignore their physical size in relation to the distance between them. Then you will have to decide what that means as far as the angle of field line from the + charge to the - charge. Given the fraction, what can you figure out about the lines that go to infinity and the lines that go to the other charge? Will all of the -q lines start at the +7q charge?

3. Aug 26, 2015

### SquidgyGuff

I apologize, by the way, for posting a homework help question here (I saw the thread rules after I posted it). The question says that it can be solved by using "a wisely chosen gaussian surface that mainly follows these lines (the lines the go to infinity)." Do you know what it means by that? Thanks

4. Aug 26, 2015

### SquidgyGuff

And is it just a convention that we say that +7q will have 7 times the number of field lines of -q or is there some physical reasoning behind that?

5. Aug 27, 2015

### Korak Biswas

There is a way to define electrostatic field in terms of number of field lines. Electrostatic field at a point is defined as the number of field lines per unit area at that point. This is acceptable probably because areal density of field lines varies as $\frac{1}{r^2}$.To understand it keep a positive charge at the origin .Then large number of ($N \rightarrow\infty$) field lines will be 'emitted' from that point radially outwards. But at distance r the areal number density will be $\frac{N}{4\pi r^2}$. And as N (although very large) is constant (because there is no other source of field lines), you can say that areal number density of field lines goes as $\frac{1}{r^2}$. So you may identify it as electric field.
Now a 7units of charge creates a seven times larger field at a particular point than 1 unit of charge if they are placed at the same position. So areal number density of field lines at a particular point due to 7 units of charge will be seven times the areal number density of field lines due to 1 unit of charge. That's why total number of field lines will also be seven times larger.