# Does the electric field have infinite range?

Fields are a theoretical concept which makes it easy for us to understand or imagine various things such as how forces act. We use electric field lines to show the strength of electric fields.

So if there is only one charge (-q) and the field lines by this should be infinite, but now if I bring another charge(+q) at that infinite distance it would still attract. At first the attraction would be slow and then it would keep increasing and eventually reach -q. If this is correct then my question would make sense

Q.) If we keep a charge somewhere on Earth, then why doesn't it get attracted by another opposite charge placed somewhere else in the world? Would this same argument work for space?

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 don't understand it; is there a way to know when the field will end (become zero), or whether the field is never-ending (infinite)?

• I find all answers to your question completely unsatisfactory, so I asked it differently here Apr 15 '20 at 16:08

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.

• Thanks. you said: "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." but even if the object gets attracted/moves towards the charge by a small distance(due to the force) it would eventually reach the main Q charge as the more it moves forward the stronger the field gets. I dont know what i am missing here, maybe something about force
– User
Apr 14 '20 at 14:22
• If the force is non zero then it will eventually move the object. But my statement is a relative one. If the force is 10^(-100000000000000000000000000000000000.....) it may take billions of years for the Q to move enough for you to measure it, and you won't live that long. In the limit of r --> infinity the force does go to zero. But as a mathematical statement infinity if not a true point, one that cannot be reached.
– user196418
Apr 14 '20 at 17:34
• @User, it is not my intent to be vague or contradictory. Depending on how far along you are with math you can estimate these things and see for yourself that they are negligible.
– user196418
Apr 14 '20 at 17:35

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.

• Screening only works inside the screening medium. The full field reappears at the boundary of the medium, in agreement with Gauss's law. Also, inaec the medium the range is still infinite unless there is extinction. Apr 14 '20 at 20:07
• That's got me thinking -- does the electromagnetic force disturb space-time like gravity does? Apr 15 '20 at 4:11
• "There's usually other stuff around and all stuff is made up of positive and negative charges" Not all stuff. Dark matter isn't, and there are electrically neutral particles like the neutron. Apr 15 '20 at 5:06

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.

As others have noted, the force is nonzero at any finite distance, but if it's small enough other forces will dominate and obscure it. For example, I can't make an object move from such a force alone if the friction it encounters in motion is larger. Even in outer space, there is a very weak braking force from the nonzero density of matter, not to mention any other forces that may act on the charge. In particular, a negligible force may not even eventually causes a collision. Gravity is much the same: A won't measurably influence B gravitationally if nearby C is enough orders of magnitude more important.

A further similarity electrostatics has with gravity is that they act on a time delay, given by the speed of light. Any gravity the Milky Way feels from Andromeda is towards where Andromeda was 2.2 million years ago; any gravity Andromeda feels from the Milky Way is towards where it was 2.2 million years ago. Needless to say, this further complicates the "eventual collision" idea for some body pairs. As it happens, these galaxies will eventually merge, with few if any star-star collisions due to their low number density. Sure, each star in the new merged galaxy will gravitationally influence each other, but that doesn't mean any given pair will eventually collide. (If anything, stars' collision fate is to merge with a supermassive black hole in the centre of the galaxy.)

On extremely large scales, electrostatics is if anything less notable than gravity, because cancelling charges cause the net charge of large bodies to be negligible compared with their mass.