Ch 22 Gauss_2009 - Gauss’s Law In this chapter you will...

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Unformatted text preview: Gauss’s Law In this chapter you will learn an easier method to calculate the electric field provided the source charges have a high degree of symmetry . This new way of finding the electric field is called Gauss’s Law (though it is really equivalent to Coulomb’s Law but in a more friendly form). Gauss’s Law is more than a tool than to solve for electric fields. It helps us gain deeper insights into electric fields. But who was Gauss? To understand Gauss’s Law we first must understand Electric Flux. Flux is related to the question of: how much charge exists inside a box? One rough experimental method to determine the charge in a box is by bring a test charge q0 to the sides of the box and calculating the electric field E. E E E E E E E q F E = Knowing the dimensions of the box and E , we could begin to have a idea how much charge exists inside the box. However, to determine how much net charge actually lies inside of a volume of space we need to further develop the idea of flux. q F E = For a single positive charge we already know that the electric field points outward. Hence if we place a box (imaginary) around the charge, the electric field will penetrate the surface area in all directions. From this the outward electric flux is defined to be: E · A Where A is the total surface area and E is the electric field through it. Definition of Flux Furthermore, the more positive charge inside a volume of space, the greater the electric field emanating through the surface. Hence the greater the flux E·A . Negative charge produces inward flux. The more negative charge the greater the inward electric field through the surface, hence the greater the flux. Flux comes from the Latin word meaning flow: flow of Electric field through the surface. It is important to choose a surface area A that matches the shape of the charge distribution so that E is a constant on this surface area. Obviously, if there are no charges in the box there will be no electric field through the surface… (provide there are not charges outside the box either or changing magnetic field…but that story comes later). Closer Look at Flux In this chapter we are considering only the electrostatic case (no moving charges or changing magnetic fields) As we have shown in the previous chapter, the electric field, due to two charges is not zero ( dipole ) however the flux will be shown to be. The net charge cancels as does the flux. This will be important in understanding Gauss’s Law 3 3 2 2 y p y qd E y πε πε = = E-field dipole Flux is like water flow, just as much electric field flows out as it flows in. For opposite charges The two fluxes add to cancel: EA – EA = 0 . As we move away from a point charge the electric field decreases as 1/r 2 ....
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This note was uploaded on 10/05/2011 for the course PHYS 4B taught by Professor W.christensen during the Summer '09 term at Irvine Valley College.

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Ch 22 Gauss_2009 - Gauss’s Law In this chapter you will...

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