lab 3-241 - Matt Weiner Phys. 241 Lab Lab Partner: Phillip...

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Matt Weiner Phys. 241 Lab Lab Partner: Phillip Hoffman 9/19/06 Field Mapping Goal: To investigate some aspects of the electric field and the electric potential for several arrangements of electrodes. Theory: If one knows the voltage everywhere, one convenient way to describe the voltage is to indicate surfaces where the voltage or electric potential is constant. The surfaces are called equipotential surfaces, because the potential is equal everywhere on one of these surfaces. d F W E P = = . . (1) The electric field is perpendicular (normal) to the electrical equipotential surfaces. There is no force on a charge in the direction along the surface just like there is no gravitational force trying to accelerate an object in a direction parallel to a level floor. The electric field is perpendicular (normal) to the electrical equipotential surfaces. There is no force on a charge in the direction parallel to a level floor. The distance between these equal voltage-spaced equipotentials is inversely proportional to the magnitude of the electric field. If the x-y plane is an equipotential surface and V is the voltage difference between two equipotentials and z is the difference between the equipotentials then: z V dz dV E z = = ; 0 = = y x E E (2)
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A positive charge experiences a force in the direction of the electric field vector E . Thus E points in the direction of decreasing potential or voltage. Thus z V dz dV E z - = - = (3) The electric potentials are analogous to the height while the electric field is analogous to how steep the mountain is at a given point (its slope). Where you are standing can be quite high (analogous to a high electric potential) but fairly level (analogous to a small electric field). If the electric potential charge quickly from place to place, the electric field is relatively large. A single point charge, q, creates an electric field, r r r q E 2 0 4 1 πε = (4) To calculate the electric field from a number of point charges one does a vector sum of the electric fields that the individual charges create. ... 3
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lab 3-241 - Matt Weiner Phys. 241 Lab Lab Partner: Phillip...

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