PHYS 208 Chapter 21

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Electric Charge

Only two types: positive and negative

Same charges (++ or −−) repel each other, opposite charges (+−) attract each other.

Conductor

Materials where electric charges are free to move around through the material.

EX: metals

Insulator

Materials where excess charges placed in/on the material remains fixed.

EX: plastic, glass, ceramics

Semiconductors

Materials that act like conductors and insulators.

Electric Charge and the Structure of Matter

Subatomic particles responsible for electric charge: electrons (−) and protons (+).

Each element has fixed number of protons, but differing number of electrons results in ions:

• default neutrally charged atom has an equal number of protons and electrons (see #2 below)
• cation (positive ion) — loss of electrons
• anion (negative ion) — gain of electrons

Conservation of Electric Charge

1. The algebraic sum of all the electric charges (net charge) in any closed system is constant.
2. The magnitude of charge of an electron is equal to the magnitude of charge of a proton and is the natural unit of charge.

Rubbing an initially uncharged glass rod with an initially uncharged piece of silk fabric will result in a positively charged rod and a negatively charged piece of silk of the same magnitude. The charges are merely transferred from one body to the other.

Induction

A process by which a charged object can give another object an opposite charge without losing any of its own charge.

1. Given an uncharged object insulated from receiving or losing any charges...
2. In the presence of an external electric charge, all of the similar charges are repelled to the opposite side of the object, temporarily polarizing the object .
3. A conductor is applied to remove the repelled charge into the ground
4. The conductor is removed, leaving only the oppositely charged pole
5. The external charge is removed from the system, and the object retains a charge opposite to the external charge.

Electric Forces on Uncharged Objects

Even if the object is an insulator, its atoms become polarized. This is why uncharged objects are attracted to both positively charged objects and negatively charged objects

Coulomb's Law

The magnitude of electric force ($F$) between two point charges is directly proportional to the product of the charges ($q_{1}$ and $q_{2}$) and inversely proportional to the square of the distance between them ($r$)

$F=k\,{\frac {\left|q_{1}q_{2}\right|}{r^{2}}}$

This equation will often be written in the following form for simplification purposes in the future.

$F={\frac {1}{4\pi \epsilon _{0}}}\,{\frac {\left|q_{1}q_{2}\right|}{r^{2}}}$

Constants

• $k={\frac {1}{4\pi \epsilon _{0}}}=(10^{-7}\ \mathrm {N} \cdot \mathrm {s} ^{2}/\mathrm {C} ^{2})c^{2}\approx 8.988\times 10^{9}\ \mathrm {N} \cdot \mathrm {m} ^{2}/\mathrm {C} ^{2}$
• $c=2.99792458\times 10^{8}\ \mathrm {m} /\mathrm {s}$ (the speed of light for above equation)
• $\epsilon _{0}\approx 8.854\times 10^{-12}\ \mathrm {C} ^{2}/(\mathrm {N} \cdot \mathrm {m} ^{2})$
• $e=1.6021765314\times 10^{-19}\ \mathrm {C}$ (the charge of an electron)

Electric Field and Electric Forces

Electric Field