32 Maxwells Equations
32.1 Lorentz force equation: F = q E + q v x B ( = dp /dt by Newtons equation of motion)
Maxwells Equations
32.2 Gauss law of electricity d = qinside /0 or
where is the charge density /oE
=
32.3 Gauss law of magnetism B d = 0 or
31 Alternating Electric Currents
31.1 The General RCLV Circuit Equation (with constant voltage V0 )
Solve the general RCLV circuit: L d2q/dt2 + R dq/dt + (1/C) q = V0 This is second order linear
inhomogeneous differential equation
Use q(t) = q0 et + B F
30 Induction
30.1 Self Induction
The change in current in a wire creates a changing magnetic field on that wire and thereby creates an induced voltage
which in turn opposes the voltage that creates the original current.
Self-Inductance: the induced volt
29 Faradays Law
29.1 Faradays Law for Induced Electric Fields
Faradays discovery of induction allows the creation of voltage by moving a loop in a magnetic field Either the flux
can change due to the motion or orientation of the wire or loop or
The flux
28 Magnetic Field Sources
28.1 The Source Equation for the Magnetic Field: The Biot-Savart law:
Biot-Savart law: Magnetic fields arise from the motion of electric charge as: dB = (o/4) I ds x runit / r2 where I =
current, ds = length of wire, dB = mag. F
27 Magnetic Fields
27.1 Magnetic Fields from Natural Objects and the Environment
In early science classes we play with magnets & learn about the N & S poles Like poles (NN & SS) repel and unlike
poles (NS) attract
With iron filings on paper over a magne
26 Direct Electrical Currents
26.1 Kirchhoffs Laws:
Sum of currents entering a junction must equal the sum leaving the junction (node)
Sum of voltages across each element in any closed loop must be zero. Examples
26.2 RCV Circuit
Kirchhoffs second law
25 Electric Current & Resistance
25.1 Electric Current
When a potential difference (voltage) exists across a substance, the charges try to move to equalize it and thus a flow
of electrical charge results called an electric current.
Electrical current is
24 Capacitance
24.1 Definition of Capacitance
Take a charge Q from object A to object B, (both neutral objects) then A potential difference of V volts between A
and B will result from this action.
The more charge one carries from A to B then the greater
21 Electric Field
21.1 Description and Origin of the Electric Field Concept
Force at a distance was difficult for people to accept thus the electric field, E, was invented
The electric field at a point is the force a unit charge would experience. Show f
22 Gauss Law
22.1 Flux of the Electric Field and Gauss Law
The flux of a vector field, V, through a surface of area A is = V * A
Gauss law states that the flux of the electric field through a closed surface is = qinside /0
A more formal vector calculus
Electromagnetic Theory
Electricity
20 Electric Forces
20.1 Fundamental Terms for Electrical Charge, Conductors, & Insulators
We are all familiar with static electricity, lightning, and electrical currents from an early age.
We are familiar with sources
33 Solution in a Vacuum EM Waves
33.1 Overview of Maxwells Discovery
Maxwell solved his equations in a vacuum meaning no charges or currents and found:
With oscillating E & B perpendicular fields at any frequency, & any amplitude with E = cB
The oscill
Light & Optics
34 Reflection of Light & Mirrors
34.1 Plane Mirrors
The law of reflection is that the angle of incidence equals the angle of reflection i=r
Flat Mirrors The left and right handiness is reversed in a mirror (eg with handwriting)
A reflect
23 Electric Potential & Potential Energy
23.1 Introduction
The potential energy of a system is the work necessary to assemble them from infinity The potential energy, U, is a
scalar and is measured in units of Joules
The electric potential V(r), is the
41 Nuclear Theory & Radioactivity
41.1 Nucleons:
Nucleons are protons or neutrons the particles that make up the nucleus of the atom The neutron was discovered in
1932 by Chadwick The neutron has a mass slightly larger than the proton
The atomic number,
40 Atomic Theory
40.1 The Model of the Atom: Prior to 1911 and afterward:
The Thompson model of the atom held that positive charge was spread out like a pudding.
In 1911 Rutherford scattered particles from gold foil and obtained large deflections. This
39 Foundations of Quantum Mechanics Particles & Waves
39.1 Cavity Radiation - Plank
Cavity radiation refers to EM radiation from a hole inside a substance -also called blackbody radiation
Is dependent upon the temperature and independent of the substanc
38 General Relativity & Astrophysics 1916
38.1 Foundational Need for General Relativity
Special relativity addresses observers moving with relative constant velocity only
General relativity deals with cases where one observer is accelerated relative to
37 Special Relativity 1905
37.1 Michelson Morley Experiment c is constant!
Constancy of c, the velocity of light, to all observers presents a conflict between Newton & Maxwell Maxwell EM
equations predict c = (00)-1/2 = 3E8 m/s in vacuum This is true to
36 Interference & Wave Nature of Light
36.1 Linear Superposition
Principle of linear superposition: resultant disturbance is the sum of separate disturbances
Interference is constructive if waves are in phase, destructive otherwise
Thin film interferen
35 Refraction of Light & Lenses
35.1 Index of Refraction & Internal Refraction
The Index of Refraction is ratio of the speed of light in vacuum to the speed in the substance n = c /v thus n > 1
always
Examples are diamond 2.419, Crown glass 1.523, Benze
1. Energy Units 1 Joule = F*d= Newton * Meter
1 Calorie = 4186 J = heat necessary to raise the temp of 1 Kg of H2O by 1 deg C
1 calorie = heat necessary to raise the temp of 1 gram of H20 by 1 deg C
1 BTU = 1055 J = heat necessary to raise the temp of