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Definition of a Field

Definition of a Field. Field Lines. Electric Field Lines. Definition of a Potential Surface. Motion of Particles in an Electric Field. Quiz. What is a Field? Fields are properties that change their value depending on what point in space or time you are measuring them.

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Definition of a Field

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  1. Definition of a Field Field Lines Electric Field Lines Definition of a Potential Surface Motion of Particles in an Electric Field Quiz

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

  4. Example of a Vector Field 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 11 10 11 12 5 14 4 20 5 Magnitude N 32° 41° 40° 28° 29° 47° 47° 38° 40° 30° Latitude 45° 43° 225° 2° 85° 2° 85° 315° 0° 44° Direction* W Longitude 95° 86° 83° 73° 91° 100° 106° 123° 118° 81° Units mph * Angles for direction are taken counterclockwise from East.

  5. 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.

  6. 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.

  7. Look at the example below… The first (on the left) set of field lines represents a uniform field that is twice the magnitude of the second (on the right). Both fields represent vectors that point to the right.

  8. Rules for Field Lines • All electric field lines • Point in the direction of the electric field vector at every point. • Start at positive charges or at infinity. • End at negative charges or at infinity. • Have a number entering or leaving a charge which is proportional to the charge.

  9. Here is another example… The first (on the left) set of field lines represents a radial field that is twice the magnitude of the second (on the right). The first is generated by a charge that is twice that of the second.

  10. Here is an example of how to find the direction of the electric field at a point on the filed line… Each point is tangent to the field line and points is the direction indicated by the black arrow.

  11. Positive point charges have electric field lines that point outward. Negative charges have electric field lines that point inward. The number of field lines is proportional to the amount of charge.

  12. Definition of a Potential Surface A surface is an equipotential surface if the electric potential at every point on the surface is the same. As charges move on an equipotential surface the electric force does no work. The electric field at a point is always perpendicular to the equipotential surface on which the point lies. The electric field always points in the direction of decreasing potential.

  13. Rules for Potential Surfaces • All electric potential surfaces • Are perpendicular to the electric field. • Decrease in value as you move in the direction of the electric field. • Are often evenly spaced in terms of potential so that the distance between them is proportional to the magnitude of the electric field.

  14. Rules for Motion • When subject to an electric force • positive charges • Move in the direction of the electric field. • Move from higher to lower potential. • negative charges • Move opposite the direction of the electric field. • Move from lower to higher potential.

  15. The electric field lines follow these five simple rules... • The number of field lines entering or leaving a charge is proportional to the absolute value of that charge. • The field lines leave positive charges and enter negative charges. • The field lines never cross each other. • Field lines are closer to each other where the field has a larger magnitude and farther from each other when the field has a smaller magnitude. • Charges follow the field lines (positive charges in the same direction as the field lines, negative charges opposite to them)

  16. Quiz

  17. If I have two charges as shown and the value of charge A is 2 μC, what is the value of charge B? A B Answer: μC -3

  18. Which is not a correct way to draw field lines? A. B. C. D. Answer: D

  19. Where is the field the strongest? C. A. D. B. Answer: C

  20. Which way will the electron initially accelerate? • Up • Down • Left • Right Answer: A

  21. Gauss’s Law follows these three simple rules... • By definition, flux is given by the equation Φ = EA cos(φ). • It also follows Gauss’s equation Φ = 4π k Qinside. • The electric field inside the material of a conductor is zero.

  22. What is the flux through the surface shown assume that the particles are electrons and protons? Answer: x 4πke -1

  23. What is the flux through the surface shown assume that the particles are electrons and protons? Answer: x 10-8 Nm2/C 3.62

  24. A charge of -2e is added to the spherical shell. Where does that charge go? • It evenly distributes in the shell. • It goes to the inside surface of the shell. • It goes to the outside surface of the shell. • Some will be on the outside surface and some on the inside surface of the shell. Answer: C

  25. A charge of -2e is added to the spherical shell. A charge of 16e is placed inside the shell. Where does the charge in the shell go? • It evenly distributes in the shell. • It goes to the inside surface of the shell. • It goes to the outside surface of the shell. • Some will be on the outside surface and some on the inside surface of the shell. Answer: D

  26. A charge of -2e is added to the spherical shell. A charge of 16e is placed inside the shell. How much charge is on the inside surface of the shell? Answer: e -16

  27. A charge of -2e is added to the spherical shell. A charge of 16e is placed inside the shell. How much charge is on the outside surface of the shell? Answer: e 14

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