Electric fields and electrical potential lab reprot

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Electric Fields and Electric Potential Introduction In this lab you will map out electric potential (V) around electrodes in a water bath. This is done by measuring the voltage drop between one fixed location and a large number of various locations in the water. From these measurements you can also determine the associated electric field. Text Reference: Young and Freedman §§21.4; 21.6; 23.2; 23.4-5. Theory In this experiment you will study the relationship between electric potential V and the electric field E. The electric field vector always points from high potential to low potential, and in this lab you will learn that, roughly speaking, the electric field strength E (the magnitude of the electric field vector E) at any point of interest can be easily calculated from a map of the electric potentials by taking the potential difference between two closely-spaced points on either side of the point of interest and dividing it by the distance between those two closely-spaced points. This description of the relationship between E and V is quite rough; but after completing this lab, you should be able to explain exactly how to calculate the electric field strength (E) and the direction of E from any detailed potential map. The electric field due to highly symmetric charge distributions can be determined using Gauss’s law. For a long, straight wire the electric field can be derived: 𝑬= Where k = * +,-. $%& ' 𝑟̂ (1) and 𝜖0 is the permittivity of free space, 𝜆 is the charge per unit length of the wire, r is the distance from the center of the wire to the field point, and unit vector 𝑟̂ gives the direction of the electric field. If the electric field E between two points a and b is known, then the potential difference between those two points can be calculated as follows: 9 Δ𝑉 = − ∫: 𝑬 ∙ 𝑑𝒍 (2) where the quantity 𝑑𝒍 represent the path taken between the points a and b. This relationship can also be inverted and the components of the electric field can be expressed in terms of derivatives such as
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