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# Physics II: ElectroStatics PHYS 2020

Marketplace > Tennessee State University > Physics 2 > PHYS 2020 > Physics II ElectroStatics
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These notes cover a basic understanding of Electric Fields, Gaussian surfaces, and Coulomb's law. I have written most of this in my own words and re-typed it in word. University Physics 13th edit...
COURSE
Physics 2
PROF.
Dr. Geoffrey Burks
TYPE
Class Notes
PAGES
16
WORDS
CONCEPTS
Physics Physics 2
KARMA
25 ?

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## Popular in Physics 2

This 16 page Class Notes was uploaded by Lauren Adams on Thursday January 28, 2016. The Class Notes belongs to PHYS 2020 at Tennessee State University taught by Dr. Geoffrey Burks in Fall 2014. Since its upload, it has received 26 views. For similar materials see Physics 2 in Physics 2 at Tennessee State University.

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Date Created: 01/28/16
Electrostatics: Chapters 21­22 Tuesday, September 9, 2014 2:44 PM Some things to explain in detail: A test charge is one that is small enough so that the charge configuration you are looking for is not disturbed.  If you were to bring a 1μC charge up against some giant 1C charge, the smaller "test" charge would not really affect the  position of the charge configuration you're studying. This leaves the equations dipole mentioned fairly easy to deal with.   If, on the other hand, you put two 1C charges in proximity (or any charge of similar magnitude), the charge configuration  will feel a strong enough force from the "test" charge that it will begin to move. If your charges move, your positions are  no longer time­independent and the system becomes far more challenging to analyze.  From <https://www.physicsforums.com/threads/what-is-point-charge-and-test-charge-why-coulombs-law-is-for-point-charges-only.611066/> A point charge, however, is a charged entity which occupies a single minute point (ideal conditions) in space. For  practical purposes we can consider any tiny charged body as a point charge, an object where all the charge is concentrated at one single point. Using point charges in basic derivations of electrostatic equations such as Coulomb's and Gauss's law eliminates the  complexities of distribution and  concentration of charge over the charged body.    The Beginning Benjamin Franklin was the first to realize there are two types of electric charge: positive, +; and negative, ­.   Charges  Like charges repel, unlike charges ttract  Are quantized. Meaning: the fundamental unit of charge ise  and charge is but a multiple ef  .  e = 1.60219 x 10­1 Coulombs, C. Conductors = materials where electric charges can move freely due to low internal resistance. (copper, aluminum, silver).  Insulators = materials where electric charges do NOT move freely due to high internal resistance. (glass, rubber). Semiconductors = conductors + insulators. Grey area. (silicon, germanium.)   An object can be charged by either conduction or induction.  Conduction = charge through direct contact between charges.  Induction = charge exchange with no contact. Happens when one charged object creates an electric field which  induces charge on a second object due to polarization.    Coulomb's Law The electrical force between two charged objects is directly proportional to the product of the quantity of charge  on the objects and inversely proportional to the square of the separation distance between the two objects. This  electrical force is attractive if the charges are of the opposite sign and repulsive if the charges have the same sign. The formula:   Electric fields    Charges produce electric fields.    They point  away  from positive charges and  towards  negative charges.                                Formula; measured in N/C     If Q is positive, then E is positive and points radially ard away  from the charge.  If Q is negative, then E is negative and points radially ard t wards  the charge.    Electric Field Lines: Things to know    The electric field vector,  , is tangent to the electric field lines at each point.  E  is large when field lines are close.   is small when field lines are far apart.  begin end  The lines must   on positive charges or at infinity and must   on negative charges or infinity.   Doubling the number of lines leaving a positive charge or approaching a negative charge, doubles the magnitude of the charge. Lines drawn with a factor of n­lines per unit volume changes the magnitude of charge by a factor of n.  Field lines ANNOT  cross each other. Two positive charges Equal and opposite charges = dipole   Conductors and Electric fields   Remember, conductors allow electrons to move freely inside the material.  No net motion of charge occurs in a conductor. Some useful facts to remember:  The electric field is 0 everywhere inside the conductor.  Any excess charge on an isolated conductor resides entirely on its surface  The electric field just outside a charged conductor is perpendicular to the conductor's surface.   On an irregular shaped conductor, charge accumulates at its sharpest points.     Electric Flux and Gauss's Law Electric Flux is a measure of the number of electric field lines that cross a given area.   Formula;  = E•A   There are several different equations for the electric flux depending on the situation in which it is produced. When the area becomes a closed surface, the flux lines passing into the interior of the volume are negative and those  passing out of the interior of the volume are positive.             Gauss's Law   The electric flux through any closed surface is equal to the net charge Q inside the surface divided by the  permittivity of free space. The total electric flux through a closed surface is equal to the net electric charge inside the surface, divided by the permittivity of free space, ε .  0   What does this really mean? Gauss's law is just a relationship between the distribution of electric charge and the resulting electric field. The net number of electric field lines passing through a Gaussian surface is proportional to the total charge enclosed by the Gaussian surface. A Gaussian surface is any closed surface which contains a volume. It can be in any shape, but cylinders and spheres are the most common types. Gauss's law is equivalent to Coulomb's law because it is just an observation based on field  lines, and field lines are  geometrical representations of  Coulomb's law.  Since most objects do not have uniform charge distributions, we must be concerned with charge densities. There are three types  worth looking into:    It is always very important to visualize the electric field lines through a Gaussian surface. If the field lines enter and leave the  surface, then there is no electric flux in the surface. If there are equal and opposite charges inside the surface then there is no  electric flux. A Gaussian surface can be whatever you imagine!        (left) Example of  zero electric  Flux inside a  Gaussian  surface.     (right) The only closed surfaces  That have zero net electric Flux are surfaces C & D.    The electric field can be simply thought of as the number of  Lines per unit area. The number of electric field lines that penetrates a given surface is called and electric flux, denoted by Φ.  The area we are talking about is the vector area or surface area in vector form. Both the vector area and electric field lines both  can point radially outward or inward depending on the electric charge that causes them. The electric flux Φ  is positive ifEthe  electric field lines are leaving the surface and negative if the electric field lines are entering the surface.  In general a Gaussian surface that is curved will have an electric field that may vary over the surface. In order to calculate the  electric flux, we have to divide the surface into a large number of infinitesimal area elements. It is best to select a surface in  which the electric field and the area create a simple electric flux that can be computed easy with surface integrals.   The electric flux can be calculated by using surface integral: Typically, though, Gauss's law is used to find the electric field through a Gaussian surface of several sorts of charge distributions. There are several different charge distributions for which the electric field can be found by applying Gauss's law: Uniform Line Charge         Infinite plane sheet of charge     Oppositely charged parallel conducting plates     Uniformly charged sphere   Say we are talking about a spherical conductor; On the inside of the sphere we are gaining charge as we move towards the  surface; the electric field increases. The flux inside across the Gaussian surface increases because the charge increases. On the  outside of the sphere, we are losing charge; the electric field decreases and the flux decreases.  NOTE: It is important to remember the flux lines are the same as field lines.    Gauss's Law is not useful for calculating the electric field for a right circular cylinder of radius R and height h with charge  uniformly distributed over its surface. This is because the direction of the field is different from all around the cylinder. This is  why an infinitely long cylinder is typically the best Gaussian surface to use because there are no ends and the vector area is  always parallel to the electric field and is perpendicular to the surface.      Conductors Inside a conductor, the electric field at EVERY point is zero. Any excess charge on a solid conductor is located entirely on its  SURFACE. The net charge on the surface of the cavity must be 0.  For the surface of the conductor, the electric field can be treated as the same as a point charge, as if all the charge were in the  center of the conductor. Therefore, This simply means that Since the electric field at all points within the Conductor must be zero, the electric field at all points on the Gaussian surface  must be zero. When there is a cavity inside the conductor, the surface of the cavity must have a total charge opposite to that at  the surface of the conductor, in order for the electric field to be zero at all points on the Gaussian surface.  The field at the surface of the conductor is given by:

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