Atomic structure and charge conservation

How can an object be neutral if it consists of charged particles? Count positive and negative charges separately and see what losing one electron changes.

An atom has a positively charged nucleus surrounded by negative electrons. Protons carry the nucleus's positive charge; neutrons are electrically neutral. One proton and one electron have charges of equal magnitude, so equal numbers of protons and electrons give a total of zero. This is a neutral atom. Neutrality means cancellation, not absence of charge. A nucleus-and-shell drawing shows composition, not the atom's actual scale.

Suppose a neutral atom loses an electron. Its nucleus is unchanged, but it now has less negative than positive charge. The remainder is positively charged and is called a positive ion. Gaining an extra electron instead produces a negative ion. Check the sign by reasoning: removing a negative increases the sum; adding a negative decreases it. Ordinary charging changes electrons, not the composition of the atomic nucleus.

Can charge be transferred in arbitrarily small amounts? Ordinary experiments transfer whole numbers of electrons or ions. The magnitude of electron and proton charge is the elementary charge e ≈ 1,6·10⁻¹⁹ Кл. An electron carries −e and a proton +e. This value is tiny, so a macroscopic object's charge comprises an enormous number of units. The symbol e denotes a positive magnitude; the particle's sign is written separately.

If n electrons pass between objects, the magnitude of transferred charge is ne. Twice as many electrons transfer twice as much charge; at n = 0 there is no transfer. But n must be an integer: this process does not produce half an electron. Dividing a large object's charge between two objects divides a collection of carriers. It cannot give an arbitrary fraction of an individual electron's charge.

Track two objects as one system. An electron leaves the first and arrives at the second: their total-charge changes are opposite. Thus, in a system exchanging no charge with its surroundings, the algebraic sum of charges is conserved. Algebraic means including signs: +q and −q sum to zero although each is nonzero. Contact may change the distribution but cannot create net charge from nothing.

A charged metal object touches Earth and nearly discharges. Has the law failed? No: we counted only the object, while carriers could move into Earth or arrive from it. One object's charge need not stay constant when it exchanges charge. Include everyone involved in the exchange and conservation is restored. Before adding charges, identify the boundary through which carriers may have passed.

Isolated objects have charges +5 nC and −2 nC. What is their total charge after contact?

Add the initial charges algebraically: +5 + (−2) = +3 нКл. Negative charge cancels part of the positive charge.

The objects are isolated from their surroundings, so contact can only redistribute this +3 nC, not change the total.

The total alone cannot determine each object's final charge: their shapes, sizes and positions are also needed.

Total charge: +3 nC. The isolated pair retains the same net positive charge after contact.

Neutral matter contains charges that cancel in the sum.

Losing an electron makes a neutral atom a positive ion; gaining one makes it a negative ion.

The signed sum is conserved in a system with no charge transfer across its boundary.

Next, use charge to calculate interaction forces and introduce a quantity describing the electric field.