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