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Ch22Sp09AGM - C hapte 22 Ele r ctric Fie lds Que stions to...

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Chapter 22: Electric Fields Questions to Answer o What is an electric field? o When is theconcept of an electric field useful? o How do you calculatethenet electric field at a point in spacedueto a system of charges? o What is an electric dipole? Why is it important? o What is theelectric field for a dipole: along the axis, and perpendicular to theaxis. o How do you calculatethenet electric field at a point in spacedueto a continuous distribution of charge? o What is thenet electric field dueto a planeof charge? Why is it important?
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1 2 2 1 4 o q q F r πε = The Electric Field The Electric Field In Ch. 21 we discussed Coulomb’s law that gives the force on a particle 2 of charge q 2 when the particle is placed near a particle 1 of charge q 1 : A question arises: how does particle 2 “know” of the presence of particle 1 ? How can there be “action at a distance”? The answer to this question is that particle 1 sets up an electric field in the space surrounding itself. The particle 2 “knows” of the presence of particle 1 because it is affected by the electric field that particle 1 has created. E F The idea of electric field was introduced by Michael Faraday in 19 th century.
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Examples of Fields Scalar fields Vector fields http://deltaklub.szm.sk/articles/a_thermal_en.htm http://www.nat.vu.nl/~pwgroen/scivis/examples.html Transient Fluid Flow in a Continuous Steel-Slab Casting Mold Temperature variation during bubble formation
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How can we calculate Electric Fields? Keep in mind analogy with gravitational force: Gravitational Force Electric Force 1 2 2 12 12 m m F G r r = - uu $ 1 2 2 12 e 12 q q F k r r uu $ = m 2 m 1 r 12 q 2 q 1 r 12
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Many of the problems we solve with the gravitational force are for masses on earth and we say there is a force on the mass due to the earth’s gravitational field: g F mgr mgj = - ⇒ - $ $ earth 2 earth g m gj G j R F m - = - = $ $ u r - $ We usually just say that the gravitational field “points down”, Here we will say that is the minus y direction. What is g ? m
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Why do we use g? We can do the same thing with the force due to electric charges, and simplify our calculations of the net force on “test” charges. The electric field at a point in space is defined as: E u e 0 F E q = u u Units? Units N/C Field exists whether or not test charge is there Test charge is considered small enough so it does not disturb the initial charge configuration
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In-Class Example: point charges
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0 e e 2 e 2 qq F k r r q E k r r = = $ u $ is vector pointing from q to q o r $ How do we calculate the magnitude and direction of the electric field? Force of charge q on test charge q o
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A charge q creates an electric field vector E at each point P in the space around q. Definition of E: We place at P a “test charge” q o with the following properties 1. It is positive q o > 0 2. q o << q This is because we do not want the electric field due to q o to distort the electric field created by q units for E: N/C o F E q u u F E r q o q
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