Transcript Gauss`s Law
Chapter 15 Electric Forces and Electric Fields General Medical Physics Physics Gauss’s Law Sections 7-9 General Medical Physics Physics What is the difference between Electric Field (E) and Force (F)? 45 7 8 9 10 21 22 23 24 25 26 27 28 29 30 11 12 13 15 .. r. 2) 16 General Medical 17 1) o nd ef in ed 14 th er 6 25% 18 Ne i 5 sd 4 Ei 3 25% 1) a ... so ut to r 2 Ef ac 1 25% e. .. 25% Bo th 1. E factors out the magnitude of the test charge, it only depends on the other charges 2. E is defined everywhere, F only at one point 3. Both 1) and 2) 4. Neither 1) or 2) 19 20 Physics Physics Review • Corn Field: corn at regularly space intervals • Vector Field: a vector at each point in space • Scalar Field: a number at each point in space – Eg: Temperature General Medical Physics Physics Review • Electric Field field • Field lines: an easy way to visualize fields – Tangent to E – Density of lines proportional to E • begin at (+), end at (-) • # of lines proportional to q • lines don’t cross General Medical Physics Physics Review • Conductors & Electrostatic equilibrium – – – – E=0 inside a conductor excess charge lies on outer surface E is perpendicular to surface charge is greatest at highest curvature General Medical Physics Physics Why are you safe inside a car during a thunder storm? 45 1. The rubber tires insulate the car from the ground 2. Charge cannot come inside the metal shell of the car 3. The rounded car has a lower charge density 4. It’s not safe! 5 6 7 8 9 10 21 22 23 24 25 26 27 28 29 30 11 12 13 15 16 General Medical 17 sa fe ! no t It’ s ro un de d ca ... ca rg e 14 Th e 4 Ch a 3 nn ot tir ... ru bb er 2 Th e 1 ... 25% 25% 25% 25% 18 19 20 Physics Physics Millikan Oil-Drop Experiment Active Figure: The Millikan Oil-Drop Experiment • Millikan Oil-Drop Experiment – Found every charge had an integral multiple of e (q = n e) – Measured the elementary charge, e = 1.610-19 C Equilibrium Drag -- Terminal velocity General Medical Physics Physics Van de Graaff Generator • An electrostatic generator designed and built by Robert J. Van de Graaff in 1929 • Charge is transferred to the dome by means of a rotating belt • Limited by ionization of air, which carries charge away • Eventually an electrostatic discharge takes place MU28T33 General Medical Physics Physics Museum of Science, Boston General Medical Physics Physics Holifield Radioactive Ion Beam Facility Oak Ridge National Laboratory 25.5 MeV General Medical Physics Physics Electric Flux • Field lines penetrating an area A perpendicular to the field • The product of EA is the flux, Φ (the number of field lines!) • In general: ΦE = E A cos θ General Medical Physics Physics Electric Flux, cont. • ΦE = E A cos θ – The perpendicular to the area A is at an angle θ to the field – When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive General Medical Physics Physics Gauss’ Law • Gauss’ Law: the electric flux through any closed surface is proportional to the net charge Q inside the surface E EA cos Qinside surface 0 – εo=8.85 x 10-12 C2/Nm2 is the permittivity of free space – The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical object Active Figure: Electric Flux Through an Arbitrary Closed Surface MU29T17 General Medical Physics Physics Electric Field of a Charged Thin Spherical Shell • The calculation of the field outside the shell is identical to that of a point charge Q Q E ke 2 2 4r o r • The electric field inside the shell is E = 0 MU29T23 General Medical Physics Physics Electric Field of a Nonconducting Plane Sheet of Charge • Total charge Q is uniformly distributed over surface A • Charge density σ = Q/A • Use a cylindrical Gaussian surface • The flux through the ends is EA, no field through the curved part of the surface E 2 o • Note, the field is uniform General Medical Physics Physics Electric Field of a Nonconducting Plane Sheet of Charge, cont. • The field must be perpendicular to the sheet • The field is directed either toward or away from the sheet General Medical Physics Physics Parallel Plate Capacitor • The device consists of plates of positive and negative charge • The total electric field between the plates is given by E o • The field outside the plates is zero General Medical Physics Physics What is the total electric flux through the surface of the cube in a constant electric field E? 45 10 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 General Medical 17 18 19 E 9 20% 6 8 2 7 EL 6 20% 20 2 5 2 4 EL 3 20% 6 2 L2 1 20% E 0 E L2 6 E L2 2 E L2 6E 0 1. 2. 3. 4. 5. 20% Physics Physics Maxwell’s Equation #1 or TIME or SPACE They all mean the same thing. General Medical Physics Physics