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Transcript
Physics 212 Electric Fields TOC Definition of a Field Field Lines Electric Fields Superposition Relationship to Electric Force Field as a Physical Property 1 Physics 212 Electric Fields Field TOC The influence of some agent, as electricity or gravitation, considered as existing at all points in space and defined by the force it would exert on an object placed at any point in space. http://www.infoplease.com/dictionary/field Fields are things which change their value depending on what point in space or time you are measuring them. They may depend on direction (vector fields) or they may not (scalar fields). Examples of Fields: 2 Temperature Profile (scalar) Wind Velocity Profile (vector) Physics 212 Electric Fields Definitions TOC Magnitude: The amount of a quantity represented by a vector or scalar. Direction: The angle of a vector measured from the positive x-axis going counterclockwise. Scalar: A physical quantity that has no dependence on direction. Vector: A physical quantity that depends on direction. Field: A set of an infinite number of related vectors or scalars found at every point in space and time. Units: A standard quantity used to determine the magnitude of a vector or value of a scalar. 3 Physics 212 Electric Fields Example of a Vector Change Wind Speed TOC Wind Velocity is a vector Its magnitude is changed when it increases and decreases its speed. Change Wind Direction Its direction is changed when it changes the compass angle toward which it blows. Graphical Representation N Real Life Mathematical Representation Magnitude 24 18 12 6 w e Southeast Northwest Northeast Direction Southwest 4 Units mph s Physics 212 Electric Fields Example of a Scalar TOC Temperature is a scalar Its magnitude is changed when it heat is added or taken away. Change Temperature It has no direction. Real Life Graphical Representation Degrees C Mathematical Representation 5 Magnitude 100 75 50 25 0 Direction none Units degrees F Physics 212 Electric Fields Example of a Vector Field TOC Wind Velocity is a function of position. This position is given by the latitude and longitude of the vector’s tail. Graphical Representation N Mathematical Representation Position 6 Magnitude Latitude 28° 40° 41° 32° 30° 29° 47° 38° N Longitude 100° 106° 123° 118° 81° 86° 83° 73° 95° 91° W 14 12 10 20 11 5 4 6 Direction* 315° 225° 85° 45° 43° 44° 0° 2° Units mph * Angles for direction are taken counterclockwise from East. Physics 212 Electric Fields Example of a Scalar Field TOC Temperature is a function of position. This position is given by the latitude and longitude of the point where the temperature is taken. Graphical Representation N Mathematical Representation Position 7 Magnitude Latitude 28° 40° 41° 32° 30° 29° 47° 38° N Longitude 100° 106° 123° 118° 81° 86° 83° 73° 95° 91° W Direction Units 51 48 75 62 58 82 74 65 87 none degrees F Physics 212 Electric Fields TOC Wind velocity can be represented by placing arrows at many locations. Each arrow represents the value of the velocity at the location of the tail of the arrow. The direction of the arrow gives the direction of the wind velocity. The length of the arrow gives the magnitude of the wind velocity. 8 Physics 212 Electric Fields The wind velocity can also be represented by lines. TOC The lines do NOT connect the arrows! The lines are closer together where the magnitude of the wind velocity is greater. The direction of the wind velocity at a point on any line is tangent to the line. 9 Physics 212 Electric Fields Electric Fields TOC Consider two positive charges, q0 and q1. The force from q1 on q0 is given by Coulomb’s Law. F1,0 k q1 q0 r1,0 2 q1 q0 k 2 r 1,0 This last equation is true regardless of the value of q0. q1 10 q0 F1, 0 Physics 212 Electric Fields Electric Fields TOC We could now divide by q0 and this is what we call the electric field at the point where q0 used to be. q1 q q 1 k 0 E F1,0 k 1,0 2 r 2q0 r1,0 1,0 q1 k 2 r1,0 Notice that it no longer depends on the value of q0. It depends only on a position. q1 11 q0 EF1,0 1, 0 Physics 212 Electric Fields Electric Fields TOC For a point charge, the electric field changes only with its distance from the charge. E1,0 q1 k 2 r1,0 It gets smaller as you move away from the charge. q1 12 Physics 212 Electric Fields Electric Fields TOC If we draw the filed lines, we can see that they get less dense with distance E1,0 q1 k 2 r1,0 The number of lines is proportional to the amount of charge. q1 13 Physics 212 Electric Fields Electric Fields are fields which add as vectors TOC Electric fields add the same way electric forces do, as vectors. The electric field is different at different locations. The magnitude of the electric field for a point charge is E1, 0 q1 k 2 r1,0 where 0 tells us the position at which the measurement is being taken. 14 Physics 212 Electric Fields TOC Finding Electric Force To find the force exerted by q1 on another charge q0, use the equation F1,0 q0 E1,0 where E1,0 is the electric field at the point where the charge is found. 15 Physics 212 Electric Fields TOC Electric Field is a physical property of a particle with charge Electric field is something we can measure independent of other charges. For a given particle, the electric field around it never changes unless we physically change the particle. Electric fields have their own energy and momentum. We can talk about the electric field even when the charge that causes the field is unknown. 16 Physics 212 Electric Fields TOC Definition of a Field Field Lines Electric Fields Superposition Relationship to Electric Force Field as a Physical Property 17