# Does the electric field have infinite range?

Q.)If we keep a charge somewhere on earth/ then why it doesnt get attracted from other opposite charge placed somewhere else in the world? Would this same argument work for space?

You are assuming the answer is "It doesn't get attracted from other opposite charge placed somewhere else..." and asking us to explain why.

In fact all charges are attracted/repelled by all other charges! Why wouldn't they be? All matter is made of charges and when you place a charge somewhere on Earth it will polarize the matter near it, e.g. the table, the ground, whatever it is near and that will cause attraction too. If you had a +Q charge in NYC and a -Q charge in Hong Kong then in theory they would attract each other. This would be true of a +Q on Earth and a -Q on the Moon. The strength of the attraction would be proportional to $$1/r^2$$ where $$r$$ is the distance between the charges. The electrostatic field does go to infinity, it is a long range force, but the strength diminishes with distance so in the limit as r --> infinity F --> 0. Charges an infinite distance away from each other would not affect each other. You may not see or sense the force due to it being weak.

You also have to consider all the other forces acting on the objects. This charge you have would presumably be in a room, a chamber, or something solid. That would potentially prevent it from moving towards (or away from) the other charge even if they were close. So everyone having charged objects lying around will not necessarily cause something to happen that we can see and measure. If you had a +Q object resting on a scale in a lab, in an enclosed box, and you placed a -Q underneath the box you should see the scale read a higher value for the weight due to the +Q being pulled down by the -Q.

I asked this question with my teacher and he said it depends on the charge whether or not its field line would be infinite or may END at some distance. I dont understand it, is there a way to know when will the field END or become zero OR the field is never ending(infinite)?

I honestly do not know how this statement related to you original question. For a free charge in space the fields will go out to infinity. If you have a collection of charges with opposite sign then field lines will leave the +Q and land on the -Q, i.e. they will "terminate". Some field will be detected at infinity due to the distribution of Q's in space, for example the pair {+q, -q} will create a dipole and E will be non-zero far away, but weak. In the presence of a conductor field lines will terminate (originate) on the conducting surface and will be perpendicular to the conductor when all Q's are in equilibrium. But none of this changes the fact the a +Q somewhere (anywhere) will attract a -Q placed somewhere else.

Yes, the electric field is infinite range. If you had an empty universe, except for two charges $$+q$$ and $$-q$$, then they would be attracted to each other and eventually collide exactly as you suggest.

But here are some caveats:

• The field decreases like $$1/r^2$$, so in practice is is very small at large distances and eventually negligible relative to other forces from more nearby objects.
• Screening:* the $$1/r^2$$ is actually a best case scenario for a charge sitting out in space all by itself. There's usually other stuff around and all stuff is made up of positive and negative charges (electrons and nuclei) that can move around and cancel out part or all of the field.

It's useful here to compare to gravity, another infinite range force that decays like $$1/r^2$$. Unlike electric fields, there is only one type of gravitational charge (all mass attracts all other mass, no repulsion). Therefore there is no screening. Most big objects in space are basically neutrally charged, so for big objects like planets the most important long-range force is gravity.

*Caveat: I may not be using screening in the most rigorous sense here.

The magnitude of the electric field will not be zero in a finite distance away from the source, but at infinite distance the magnitude of the electric field would be zero.

Answering the question, the charge will get attracted to the opposite charge on the opposite side of the Earth, and the case is that no matter how large their separation is, given the separation is finite, they will still be attracted to each other.