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## PARADIGMS IN PHYSICS STATIC VECTOR FIELDS

by: Mrs. Demarcus Breitenberg

13

0

2

# PARADIGMS IN PHYSICS STATIC VECTOR FIELDS PH 422

Marketplace > Oregon State University > Physics 2 > PH 422 > PARADIGMS IN PHYSICS STATIC VECTOR FIELDS
Mrs. Demarcus Breitenberg
OSU
GPA 3.68

Staff

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COURSE
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Staff
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Class Notes
PAGES
2
WORDS
KARMA
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## Popular in Physics 2

This 2 page Class Notes was uploaded by Mrs. Demarcus Breitenberg on Monday October 19, 2015. The Class Notes belongs to PH 422 at Oregon State University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/224539/ph-422-oregon-state-university in Physics 2 at Oregon State University.

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Date Created: 10/19/15
PH 422 Day 6 1 Dot Products and Components The previous activity used the concepts of the parallel and perpendicular components of E What are components Start in rectangular coordinates where E EziEyjEzl 2 Similarly in cylindrical coordinates E ETPE lt13E12 What is the c cornponent of E Surely just Egg The r cornponent ET How could you nd these components given E The scalar component of a vector eld in a given direction is just the projection in that direction Projections are dot products Thus V EzEi EE quot Given a surface it makes sense to ask what the component EL of the electric eld is perpendicular to the surface By the same reasoning we have EL E 71 where fl is the unit normal to the surface The parallel cornponent EH is more subtle since there are several directions parallel to the surface One often speaks of vector components for instance 17L EL 73 and we can now de ne the parallel vector component of E as EEEi from which the magnitude EH lEHl can be computed using the Pythagorean Theorern if desired 2 Currents How do we measure current By counting the charges which go past So use a stopwatch and count What are the units Coulombs per second What answer do we get That depends on the charge density A and the velocity 393 At any point in a wire the current is given by V I39B and the number of charges which go past per unit time is clearly just the magnitude I Since the direction of the current is obvious in a wire both I and T are called the current Similarly the surface current density if and the volume current density j given respectively by lt71 1 m7 2 Be very careful with the dimensions here current densities do not have the dimensions of current per unit area or volume respectively but rather the dimensions of charge density times speed But what is the total current in these cases The key idea is that one must insert a 1 or 2 dimensional gate and count the charges which cross the gate per unit time But only the motion of the charges perpendicular to the gate is relevant This is 2 and 3 dimensional ux the total current is given respectively by Lu Ni i Ru ds 3 M j M 4 Lu gt I

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