1. Electricity Electric Fields 1 TOC Definition of a Field Field Lines Electric Fields Superposition Relationship to Electric Force Field as a Physical Property

2. Electricity Electric Fields 2 TOC Field 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: Temperature Profile (scalar) Wind Velocity Profile (vector)

3. Electricity Electric Fields 3 TOC Definitions 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.

4. Electricity Electric Fields 4 TOC N Example of a Vector Change Wind Speed Change Wind Direction Wind Velocity is a vector Its magnitude is changed when it increases and decreases its speed. Its direction is changed when it changes the compass angle toward which it blows. Real Life Graphical Representation Mathematical Representation Magnitude Direction Units 24 Northwest mph 61218 NortheastSoutheastSouthwest e s w

5. Electricity Electric Fields 5 TOC Change Temperature Temperature is a scalar Its magnitude is changed when it heat is added or taken away. It has no direction. Graphical Representation Mathematical Representation Magnitude Direction Units 0 none degrees F Degrees C Example of a Scalar 255075100 Real Life

6. Electricity Electric Fields 6 TOC Graphical Representation Example of a Vector Field Mathematical Representation Magnitude Direction* Units mph N Latitude 40° 118° Longitude Position Wind Velocity is a function of position. This position is given by the latitude and longitude of the vector’s tail. 38° 32° 47° 41° 29°47°30° 40°28° 123°106°100°91°95°73°83°86°81° 10121120514 5 4116 85°2°85°2°0°45°225°315°44°43° N W * Angles for direction are taken counterclockwise from East.

7. Electricity Electric Fields 7 TOC Example of a Scalar Field Mathematical Representation Magnitude Direction Units degrees F Latitude 40° 118° Longitude Position 38° 32° 47° 41° 29°47°30° 40°28° 123°106°100°91°95°73°83°86°81° 657482586275485182 65 N W Temperature is a function of position. This position is given by the latitude and longitude of the point where the temperature is taken. none 74 82 58 62 75 48 51 82 87 Graphical Representation N

8. Electricity Electric Fields 8 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.

9. Electricity Electric Fields 9 TOC The wind velocity can also be represented by lines. 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.

10. Electricity Electric Fields 10 TOC Electric Fields Consider two positive charges, q 0 and q 1. The force from q 1 on q 0 is given by Coulomb’s Law. This last equation is true regardless of the value of q 0. q1q1 q0q0

11. Electricity Electric Fields 11 TOC Electric Fields We could now divide by q 0 and this is what we call the electric field at the point where q 0 used to be. Notice that it no longer depends on the value of q 0. It depends only on a position. q1q1 q0q0

12. Electricity Electric Fields 12 TOC Electric Fields For a point charge, the electric field changes only with its distance from the charge. It gets smaller as you move away from the charge. q1q1

13. Electricity Electric Fields 13 TOC Electric Fields If we draw the filed lines, we can see that they get less dense with distance The number of lines is proportional to the amount of charge. q1q1

14. Electricity Electric Fields 14 TOC Electric Fields are fields which add as vectors 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 where 0 tells us the position at which the measurement is being taken.

15. Electricity Electric Fields 15 TOC Finding Electric Force To find the force exerted by q 1 on another charge q 0, use the equation where E is the electric field at the point where the charge is found.

16. Electricity Electric Fields 16 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.