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I am new to electricity and this question has been bothering me. Like most of us have heard that positive and negative create a neutral object like a neutral atom and so forth. But actually, how is this achieved. How do two opposite charge come together and cancel each others charges up? Can anyone how this cancellation occur in terms of electric field lines and all. Thanks.

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First of all, physically two charges do not cancel each other. But, we often say so. That's the source of your confusion. Let me explain why it's like that, rather than explicitly answering your question. In the discussions below, I assume we deal with charges at rest w.r.t you and me.

Consider a positive charge of magnitude $q$. It has got an electrostatic field (more precisely, an electromagnetic field) of its own. Don't ask why. It's their property and we cannot question that. This electrostatic field originates from the positive charge $q$ and diverges out in space. If you consider a negative charge, but of same magnitude, you can see that the number of field lines passing through a given area placed at the same distance from the charges are the same, except the point that the electric field due to a negative charge do not diverge, but they converge into the charge. So, what I actually want you to focus upon is that the electric field has got a particular magnitude and direction. Hence it's a vector quantity. Charges on the other hand are scalar quantities.

Now, we consider a system of two charges , both of same magnitude but opposite signs- say an electron and a positron. In such a case, as you see from the above discussions that the electrostatic field of the positron (charge: $+e$) originates from it and diverges out from it. On the other hand the electric field due to the electron (charge:$-e$) converges into it. The two charges are in the vicinity of each other. So one is in the electric field due to another. Hence in effect, the field originates from the positron and it ends at the electron. The two charges hence interact electrostatically (which cannot be seen in practice and is just only a theory), whose strength is governed by the Coulomb's law in electrostatics. If the charges are too close, then the strength of attraction will be too strong. The force decays as $r^{-2}$, $r$ being the separation distance between the two charges.

Now, this interaction causes the electric field lines from the positron to be terminated at the electron. Hence no electric field line can be found around the system of the two charges (the field lines do not "leak" in the case of point charges, because fringe fields can develop at sharp edges or points), except in between the two. So, the electric field is contained (or confined) within the system of two charges. If they are very close, then you can't possibly find a space in between them to measure the electric field and it appears that you cannot find a trace of the electric field due to the system of the charges. Since there is no "net" electric field around the system, there is no "net" charge on the system (Gauss's law). Hence we have a neutral "object" (formed from two charged objects).

You may ask why it is then so contrary to speak that two opposite charges cancel each other. No objection. All I want you to remember is that it is the net charge that is zero. Individually the charges are not zero. Take the example of an ionic crystal, say $NaCl$, where $Na^+$ and Cl^-$ ions are tightly held together by electrostatic attraction. Both ions have equal and opposite charges. If the interaction between the two lead to the individual destruction of charges (losing property as a charge), then how the solid continues to be so brittle. There is always interaction between the two ions. This means the interaction between the two charges do not cause the charges to lose their charge. It's the effective charge that is zero. We then speak about a system, not about individual charges.

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In the vast majority of cases, this combination of opposite charges to create electrically neutral objects will happen "naturally", that is no human intervention is required to equalise charges, quite the reverse in fact.

If you take the number of atoms in your body, approximately $10^{27}$, and assume that even a tiny fraction of these were not neutral, you would feel the effects immediately. So equalisation of charge on atoms happens very quickly.

It is a self correcting process, the higher the positive or negative charge on an object, the more likely that electrons will be attracted or expelled from the object to achieve neutrality.

enter image description here

Look at the right hand side of the above picture, from a distance, the overall system is neutral.

If you read this site : Electrostatics

Each of the above diagrams, the individual source charges in the configuration possess the same amount of charge. Having an identical quantity of charge, each source charge has an equal ability to alter the space surrounding it. Subsequently, the pattern is symmetrical in nature and the number of lines emanating from a source charge or extending towards a source charge is the same. This reinforces a principle that states that the density of lines surrounding any given source charge is proportional to the quantity of charge on that source charge. If the quantity of charge on a source charge is not identical, the pattern will take on an asymmetric nature, as one of the source charges will have a greater ability to alter the electrical nature of the surrounding space. This is depicted in the electric field line patterns below.

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