1-1 ;;Quote: the electrical force is a billion-billion-billion times stronger than gravity; its positives and negatives balance almost perfectly forming tight, fine mixtures

1-1 ;;Quote: if two people at arm's length had 1% more electrons than protons, their repulsion would be enough to lift the earth

1-1 ;;Quote: electrical force holds atoms and molecules together; at the scale of atoms, electrical forces are not balanced

1-2 ;;Quote: the nuclear forces hold the nucleus together; much stronger than electrical force but it falls off much more rapidly than 1/r^2

1-2 ;;Quote: the energy of the atomic bomb is really electrical energy that is released when electrical forces overcome the nuclear forces

1-2 ;;Quote: the electrical force on a charge depends only on its position, velocity, and size; the equation of force is in terms of the electrical and magnetic fields which vary by position and time

1-3 ;;Quote: principle of superposition: the electric and magnetic fields produced by a set of charges is the same as their sum over each charge

1-4 ;;Quote: a field is any physical quantity which takes on different values at different points in space; e.g., electrical and magnetic fields; values may be scalars or vectors

1-10 ;;Quote: magnetism is a relativistic effect; for electrons moving in parallel wires the relativistic correction is 10^-25

1-10+;;Quote: when relativity was discovered, the electromagnetic laws already accounted for relativistic effects

5-4 ;;Quote: can use Gauss' law to approximate the electrical field inside an atomic nucleus

5-4+;;Quote: the protons are spread nearly uniformly throughout the body of the nucleus

5-5 ;;Quote: because Coulomb's force law is exactly the inverse square, a thin spherical shell of charge is like a point charge outside the shell and zero inside the shell

5-7 ;;Quote: by Gauss' law, the charge density is zero inside any conductor; any excess charge is within one or two atomic layers of the surface with the electric field normal at the surface

5-7+;;Quote: shielding: any static distribution of charges inside a closed conductor can not produce any fields outside, and vice versa

6-2 ;;Quote: a dipole is a close pair of electric charges; they occur commonly, e.g., water

6-2+;;Quote: a dipole's electric field decreases as 1/r^3 and is twice as strong on the axis as at 90 degrees to the axis

6-2+;;Quote: at a distance, any neutral collection of charges acts the same as a dipole

6-12 ;;Quote: to get a large condenser use a big area and a small separation, e.g., roll wax paper and aluminum foil for a radio-type condenser

7-8 ;;Quote: many chemical effects can be understood via electrical forces; e.g., a colloid consists of small charged particles suspended in water; salt neutralizes the charge and allows coagulation

7-11 ;;Quote: the electric fields sufficiently inside a closed screen are zero, just like a closed metal sheet

8-10 ;;Quote: can locate energy because it is conserved locally; this agrees with energy's equivalence to mass and hence gravitational forces

9-1 ;;Quote: the electric potential across the earth's atmosphere is 400,000 volts with a total electric current of 700 megawatts

9-1+;;Quote: the upper atmosphere is almost a perfect conductor

9-1+;;Quote: thunderstorms recharge the atmosphere with electrons

9-1+;;Quote: measure the electrical potential of the atmosphere by a bucket of water with a small leak

10-2 ;;Quote: a dielectric or insulator contains many dipoles; these are attracted to charged objects at the square of the electric field

12-1 ;;Quote: the equations for many physical situations have exactly the same appearance; e.g., steady heat-flow problems and electrostatic problems are the same

12-12 ;;Quote: the equations for many physical situations are similar because they depend on smooth fields in space with laws that are independent of direction

12-12+;;Quote: any simple, spatial physical problem, or simplification of a complicated problem, must look like electrostatics

13-2 ;;Quote: electric charge is conserved, i.e., it is indestructible

13-5 ;;Quote: the magnetic field outside a long straight wire is proportional to the current and inversely proportional to the distance from the wire

13-8 ;;Quote: the charge of an electron is independent of its speed, but the charge density of moving electrons varies like the relativistic mass of a particle

13-9 ;;Quote: electric and magnetic forces are part of one physical phenomenon; e.g., the magnetic force on a charge moving along a wire is the same as the electric force of a wire moving past a charge

15-7 ;;Quote: a real field is a set of numbers such that what happens at a point depends only on the numbers at that point; no action at a distance

15-8 ;;Quote: in quantum mechanics the force concept is replaced by the concepts of energy and momentum, frequencies and wavelengths

15-8+;;Quote: use vector and scalar potentials for introducing electromagnetic effects into quantum descriptions; avoids the use of force concepts

15-9 ;;Quote: a magnetic or electrical field changes the phase of the probability amplitude to arrive via any trajectory by the space or time integrals respectively

16-9 ;;Quote: the generators at Boulder Dam turn thousands of little wheels throughout the whole city; such an effect exists nowhere else in nature

18-9 ;;Quote: measure the speed of propagation of electromagnetic fields by measuring the forces between two unit charges and between two unit currents; same as the speed of light

18-9+;;Quote: Maxwell realized that light, electricity, and magnetism were the same phenomena; one of the great unifications of physics

18-9 ;;Quote: for any electromagnetic wave, the magnetic and electrical fields are perpendicular to the direction of motion, the fields are mutually perpendicular, and the magnitude of the electric field is c times that of the magnetic field

19-2 ;;Quote: the principle of least action for conservative forces: the path taken is the path with the least action; many nearby paths; e.g., the average kinetic energy less the average potential energy

19-2+;;Quote: the calculus of variations determines the path in space which minimizes the path's action

19-2+;;Quote: at the microscopic, deepest level of physics, all forces are conservative forces

20-1 ;;Quote: from Maxwell's equations: fields generated by moving charges can leave the sources and travel alone through space even after all activity has stopped and the charges are zero

20-1+;;Quote: electromagnetic waves can exist independently of any charges or currents

20-8 ;;Quote: it is harder to understand the electromagnetic field than to understand invisible angels; the former requires a vivid imagination of a myriad of complex waves

27-1 ;;Quote: energy conservation law: if energy goes away from a region, it flows through the boundary of that region; similarly, charge conservation requires a local conservation law

30-1 ;;Quote: in a solid, atoms arrange themselves in a configuration that minimizes the energy; this pattern repeats and thus forms a crystal

30-2 ;;Quote: in a molecular crystal such as sugar or paraffin the molecules keep their individual identity; the solid is easily broken

30-2+;;Quote: a diamond is really one giant molecule held together with strong covalent bonds

30-3 ;;Quote: in a metal, each atom contributes an electron to a universal pool of electrons and the atomic positive ions are often like small spheres packed in as tightly as possible

30-3 ;;Quote: in a liquid, all atoms are in perpetual motion; they bounce against their neighbors about 10^13 times per second

30-8 ;;Quote: dislocations in a crystal may get stuck at any imperfection in the crystal; e.g., steel is iron plus some carbon that prevents dislocations from moving about

41-1 ;;Quote: the velocity of a fluid is exactly zero at the surface of a solid; e.g., a fan collects dust even when moving

41-11 ;;Quote: there is tremendous variety of behavior from the equations for viscous fluid flow with just one parameter; how much more is possible with more complex equations!

41-11+;;Quote: perhaps we can write an equation for life; perhaps it is quantum mechanics; God may not be needed to explain the complexities of the world

41-11+;;Quote: the complexities of things can easily and dramatically escape the simplicity of the equations which describe them

42-1 ;;Quote: from Einstein, space-time is curved near heavy masses; gravitation is the result of going along straight lines in a curved space-time

42-1 ;;Quote: consider a bug that lives on a hot plate and uses rulers effected by temperature; if the length of a ruler varies by the square of the distance from the origin, the geometry is that of a sphere

42-7 ;;Quote: by Einstein's general relativity, the earth has 1.5 millimeters more radius than it should have for its surface area

42-7+;;Quote: space is curved, matter is the source of the curvature, and it is that curvature that we see as gravitational force

42-8 ;;Quote: straight-line motion in a curved space-time is that motion which maximizes the elapsed time of an object over some fixed local time

42-9 ;;Quote: on a rocket ship a clock at the head runs faster than one at the tail; the same thing happens in a gravitational field, the higher clock runs faster

42-9+;;Quote: an altitude difference of 20 meters at the earth's surface speeds up a clock by two parts in 10^15; tested experimentally with the Mossbauer effect

42-12 ;;Quote: in a gravitational field with given starting and finishing conditions, an object moves so as to maximize the time of a clock traveling with the object