18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

Electrical Charges and Conservation of Charge

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Properties of electric charges

Electric charge is a fundamental property of matter. It comes in two types: positive and negative. The core rule is simple: like charges repel, opposite charges attract. This single idea drives nearly everything in electrostatics.

At the atomic level, protons carry a positive charge ($+e$) and electrons carry a negative charge ($-e$). Neutrons are electrically neutral. Electric charge is quantized, meaning it always comes in integer multiples of the elementary charge:

$e = 1.602 \times 10^{-19} \text{ C}$

You can't have half an electron's worth of charge. Every charge you'll ever encounter is some whole-number multiple of $e$.

The net charge of an object is the sum of all its positive and negative charges. An atom with equal numbers of protons and electrons has a net charge of zero, making it electrically neutral. An object becomes charged only when there's an imbalance between protons and electrons.

Conservation of charge calculations

The law of conservation of charge states that the net electric charge in an isolated system remains constant. Charge is never created or destroyed; it only transfers between objects.

When two objects are brought into contact, electrons (the mobile charge carriers) move from one object to the other. This is called charging by conduction. The charge gained by one object is exactly equal in magnitude to the charge lost by the other.

To solve charge transfer problems, use this conservation equation:

$Q_1 + Q_2 = Q_1' + Q_2'$

where $Q_1$ and $Q_2$ are the initial charges on each object, and $Q_1'$ and $Q_2'$ are the final charges after contact. For two identical conductors brought into contact, the charges equalize, so each ends up with:

$Q_{\text{final}} = \frac{Q_1 + Q_2}{2}$

For example, if a metal sphere with $+6 \text{ μC}$ touches an identical sphere with $-2 \text{ μC}$, each sphere ends up with $\frac{+6 + (-2)}{2} = +2 \text{ μC}$.

Conductors vs insulators

Conductors are materials that allow electric charges to flow freely. Metals like copper, silver, and aluminum are good conductors because their valence electrons are loosely bound and can move throughout the material.

Insulators resist the flow of charge. Materials like glass, rubber, and plastic have tightly bound electrons that stay put. Charge placed on an insulator tends to remain where it was deposited rather than spreading out.

Semiconductors fall between conductors and insulators. Materials like silicon and germanium can have their conductivity dramatically changed by doping (adding specific impurities) or by applying electric fields. This tunability is what makes them essential for electronics.

Dielectrics are insulators that can be polarized by an external electric field. The charges within the material shift slightly, which affects how the material interacts with electric fields. You'll see dielectrics again when studying capacitors.

Polarization and induction charging

Electric polarization is the redistribution of charges within an object due to an external electric field.

• In conductors, free electrons physically move to one side, leaving a net positive charge on the opposite side. An electroscope demonstrates this well.
• In insulators, electrons can't move freely, but they shift slightly within their atoms, creating tiny induced dipoles. Water molecules are a classic example of permanent dipoles that also respond to external fields.

Charging by induction lets you charge an object without ever touching it to a charged object. Here's the process:

1. Bring a charged object near (but not touching) a neutral conductor. This polarizes the conductor, pushing electrons to one side.
2. While the charged object is still nearby, ground the conductor (connect it to a large reservoir of charge, like the Earth). Electrons flow in or out through the ground connection.
3. Remove the ground connection first, then remove the charged object. The conductor is left with a net charge opposite to the inducing object.

The order matters: if you remove the charged object before disconnecting the ground, the electrons redistribute and the conductor stays neutral.

Electrostatic shielding occurs when a conductor surrounds a region of space. The conductor's free charges rearrange to cancel any external electric field inside the enclosed region. This is the principle behind a Faraday cage, which protects sensitive electronics like circuit boards and shielded cables from external electric interference.

Electric Fields and Electrostatics

An electric field is a region of space around a charged object where other charges experience a force. You'll explore electric fields in much more depth in upcoming sections, but the key idea is that charges create fields, and fields exert forces on other charges.

The electromagnetic force is one of the four fundamental forces of nature. It governs all electric and magnetic interactions and is responsible for the behavior of charges described throughout this unit.

The triboelectric effect is the transfer of charge between two materials when they're rubbed together (brought into contact and separated). Rubbing a balloon on your hair, for instance, transfers electrons from your hair to the balloon, leaving the balloon negatively charged and your hair positively charged. Different materials have different tendencies to gain or lose electrons, which is summarized in the triboelectric series.