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Physics 272 January 16 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem [email protected] Phys272 - Spring 14 - von Doetinchem - 39 i>clicker GO Phys272 - Spring 14 - von Doetinchem - 40 Summary Source: http://en.wikipedia.org/wiki/Electric_charge Coulomb's law Phys272 - Spring 14 - von Doetinchem - 41 Summary Superposition of electric force Phys272 - Spring 14 - von Doetinchem - 42 Electric field and electric forces ● ● ● How do electric charges know of each others existence? What is an electric field? A single charge causes an electric field in the surrounding space If you drop a second charge in this field the two charges communicate through their fields Phys272 - Spring 14 - von Doetinchem - 43 Eletric field http://www.youtube.com/watch?v=7vnmL853784 Phys272 - Spring 14 - von Doetinchem - 44 Electric field and electric forces ● ● The fields are responsible for exerting the electric force on the other charge An electric field creates an electric force on a test charge q0 Phys272 - Spring 14 - von Doetinchem - 45 Electric field and electric forces ● ● ● The electric field concept is again analogous to the gravitational field Electrical field is useful because it does not depend on the charge of the body on which the electric force is exerted. Calculation of electric field becomes more complicated if the charged object is not point like. Field strength and direction will depend on the relative position to the object. Phys272 - Spring 14 - von Doetinchem - 46 Sharks ● ● ● ● ● ● Living objects produce electric fields due to, e.g, muscle contraction Ocean currents also produce electric fields Sharks use electroreception Source: http://en.wikipedia.org/wiki/Shark sensors are called the ampullae of Lorenzini: jelly filled canals ending in pores: small electric fields cause charge flow → trigger to nervous system Multiple sensors allow 3D sensing Also used for navigation Source: http://en.wikipedia.org/wiki/Shark Phys272 - Spring 14 - von Doetinchem - 47 Sharks A bonnethead shark biting actively and vigorously at various electric dipoles while ignoring the live fish swimming around with it. Dr. Stephen M. Kajiura, Elasmobranch Research Lab, Boca Raton, FL http://www.youtube.com/watch?v=4aYPHeK1Tyo Phys272 - Spring 14 - von Doetinchem - 48 Electric field of a point charge ● ● Electric field always points away from a positive charge and toward a negative charge Associated with one charge you do not have only one single vector, but a whole set of vectors → vector field as a function of location ● Region of the same electric field strength are called: uniform ● In other words: electric charges act as sources for electric fields ● Conductor: electric field in a conductor leads to motion of charges → electrostatics = no motion of charges → electric field in a conductor is 0 Phys272 - Spring 14 - von Doetinchem - 49 Electric field of a point charge ● ● ● What is the magnitude of the electric field at a distance for a point charge? We know the distance of the point to the charge and we know the magnitude of the charge: If you would place a second charge in the field: multiplying this result with the value of the second charge gives you the force on the second charge. Phys272 - Spring 14 - von Doetinchem - 50 Electron in a uniform field ● ● ● Release of an electron in a uniform electric field Concepts: – electric fieldelectric force relation – Force and acceleration We know the field, mass, and charge Phys272 - Spring 14 - von Doetinchem - 53 Electron in a uniform field ● ● ● Release of an electron in a uniform electric field Concepts: – electric fieldelectric force relation – Force and acceleration We know the field, mass, and charge Phys272 - Spring 14 - von Doetinchem - 54 Electric field calculations ● ● ● How to calculate fields if the charges are not pointlike? Important for many applications: trajectories of charges particles and ions, computer chips, etc. Approach: sum up fields of many point-like charges (electrons are very point-like and protons are extremely small) Phys272 - Spring 14 - von Doetinchem - 57 Charged line segment ● What is the electric field at point P along the x axis? Phys272 - Spring 14 - von Doetinchem - 63 Charged line segment ● How large is the electric field in y direction along x? Phys272 - Spring 14 - von Doetinchem - 64 Field of a ring of charge ● Integrate over may tiny rings: Phys272 - Spring 14 - von Doetinchem - 65 Field of a ring of charge Phys272 - Spring 14 - von Doetinchem - 66 Field of a uniformly charged disk ● Nonconducting disk with positive surface charge ● if the disk is large R>>x → electric field is independent of x Phys272 - Spring 14 - von Doetinchem - 67