Introduction to Electromagnetism - 11

Summary of Capacitance Formulas Review Chapter 20 (all) Check sections 20.4 and 20.5 Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 11 February 17, 2007 Dielectrics A dielectric is a non-conducting material, such as rubber, glass, or waxed paper. When a dielectric is inserted between the plates of a capacitor, the capacitance increases. Let us say that the dielectric completely fills the space between the plates, the capacitance increases by a factor k. k is called the dielectric constant. One of the effects of a dielectric is to introduce a breakdown potential, Vmax. We characterize dielectric materials with a dielectric strength, maximum value of the electric field it can tolerate (V/L). Parallel Plate Cylindrical Capacitor Spherical Capacitor With a dielectric Outside a conductor we have TYPES OF CAPACITOR Metal foil interlaced with thin sheets of paraffin-impregnated paper on mylar. The alternate layers are rolled. HIGH V capacitor interwoven metal plates immersed in silicone oil. Polar Molecule (water) Atomic view of dielectrics POLAR DIELECTRICS i.e. water, where each molecule has a permanent dipole moment. will produce alignment (partial because of thermal energy). NON-POLAR DIELECTRICS the dipole is created through induction. In an insulator, electrons are not free to move, but they will readjust within the molecule, creating a dipole. We apply an electric field Random distribution of polar molecules The dipole (induced or permanent) of the molecule will rearrange itself to produce an electric field opposite The resulting electric field will be since Eind is always opposite E0, E E0. In fact Induced charge on a dielectric placed between the plates of a charged capacitor. Note that the induced charge density on the dielectric is less than the charge density on the plates. Example 26.9 Example 26.10 ENERGY STORED Consider a parallel plate capacitor initially uncharged V 0 After connection to a battery it will develop a charge Q CV Assume the charging is done slowly. From the definition of work to move a charge across a potential difference we get The total work required to charge the capacitor is The work done in charging the capacitor can be considered as potential energy U stored in the capacitor, i.e., The energy stored in a capacitor can be considered as being stored in the electric field created between the plates as the capacitor is charged. Example parallel plate capacitor. Ad is the volume between the plates. We can define an energy per unit volume The energy density in any electric field is proportional to the square of the electric field. . Cell membrane Inside of cell h 9. When a potential difference of 150 V is applied to the plates of a parallel-plate capacitor, the plates carry a surface charge density of 30.0 nC/cm2. What is the spacing between the plates 4 19. Two capacitors when connected in parallel give an equivalent capacitance of 9.00 pF and give an equivalent capacitance of 2.00 pF when connected in series. What is the capacitance of each capacitor