Time an object under free fall gravitational acceleration g

If object falls starting from rest:

v(t ) gt

1 2 x(t ) gt

2

Plotting velocity (y axis) vs. time (x axis) should have a slope of g

Fill out pre-lab sheet available at http://physics.msstate.edu/labs

Vectors – geometric objects that are independent of any coordinate system 3

ˆ

ˆ

A Ai ei Ai ei

ˆ ˆ ei e j ij

i 1

Einstein summation convention

Scalar (or dot) product of 2 vectors

A B

AB

i 1..3

i

i

!!! Scalar quantity - invariant under the rotation of coordinate system !!!

Cross (or vector) product of 2 vectors

C A B C AB sin n

Angle b/w A and B

A B B A

Defining the direction of the normal vector in cross product

Chapter 21

Electric charge and electric field

Electricity and Magnetism, Some History: 1

• Many applications

– Macroscopic and microscopic

• Chinese

– Documents suggest that magnetism was observed as early as 2000 BC

• Greeks

– Electrical and magnetic phenomena as early as 700

BC

– Experiments with amber and magnetite

• 1600: - William Gilbert showed electrification effects were not confined to just amber

– the electrification effects were a general phenomena

Electricity and Magnetism, Some History: 2

• 1785

– Charles Coulomb confirmed inverse square law form for electric forces

• 1819

– Hans Oersted found a compass needle deflected when near a wire carrying an electric current

• 1831

– Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire

Electricity and Magnetism, Some History: 3

• 1873

– James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism • Unified electricity and magnetism

• 1888

– Heinrich Hertz verified Maxwell’s predictions

– He produced electromagnetic waves

Electric Charges: basic properties

There are two kinds of electric charges: positive – protons, negative - electrons

Particle

Symbol Charge

Mass

Electron

-1

1

Proton

p

+1

1836.15

Neutron

en

0

1838.68

The electric charge, q, is quantized

– q is the standard