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Physics 272 January 21 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 - 70 Summary ● ● The electric fields of electric charges 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 - 71 Summary ● Electric field always points away from a positive charge and toward a negative charge ● vector field as a function of location ● electric charges act as sources for electric fields ● electric field in a conductor is 0 Phys272 - Spring 14 - von Doetinchem - 72 Electric field lines ● ● ● ● A field line illustrates the direction of the electric field at a certain point If you draw the tangent to a point on a field line you get the direction of the field at this point Spacing of electric field lines is chosen such the density illustrates the magnitude Field lines do not intersect Phys272 - Spring 14 - von Doetinchem - 77 Electric dipoles ● ● ● Pair of point charges with equal magnitude and opposite sign Important from molecules to antennas Example water: chemical bounds cause displacement of charge → water is a good solvent (e.g., salt splits to Na+ and Cl- in water) → very important for biochemical reactions Phys272 - Spring 14 - von Doetinchem - 78 Water – a not so normal liquid ● One of the lightest gases known ● as a liquid much denser than expectd ● As a solid much lighter than expected ● Molecular Hydrogen bonding plays an important role ● High freezing, high melting point ● ● ● ● Large heat capacity, high thermal conductivity → body temperature control Excellent solvent due to polarity Water ionizes and allows easy proton exchange in molecules → richness of ionic interactions in biology Read more: http://www1.lsbu.ac.uk/water/anmlies.html Phys272 - Spring 14 - von Doetinchem - 79 Force and torque of an electric dipole ● Electric dipole in a uniform external field Electric dipole moment points from the negative to the positive charge Phys272 - Spring 14 - von Doetinchem - 81 Potential energy of an electric dipole φ=0: pot. energy minimal, stable equilibrium, dipole parallel to field φ=π/2: pot. energy 0, dipole perpendicular to field φ=π: pot. energy maximum, dipole antiparallel to field ● Electric-field torque does work on dipole → change in potential energy ● Dipoles try to minimize potential energy ● An uncharged object with a dipole moment can experience a net force in a non-uniform electric field (polarization can happen due to electric field) Phys272 - Spring 14 - von Doetinchem - 83 Review ● ● Electric charge, conductors, and insulators: – Fundamental quantity in electrostatics – Charge is conserved – Protons carry positive charge and electrons negative charge – Conductors are materials in which charge moves easily. Charge does not move easily in insulators. Coulomb's law: Phys272 - Spring 14 - von Doetinchem - 88 Review ● ● ● ● The electric field is the force per unit charge exerted on a test charge at any point. Electric field radially points away from point charge. Electric force and field can be superposed. Electric field lines describe direction and magnitude of the field at a certain point. An electric dipole is a pair of positive and negative charges of same magnitude, but opposite sign. Phys272 - Spring 14 - von Doetinchem - 89 Discussion 1) Your clothing tends to cling together after going through the dryer. Why? Would you expect more or less clinging if all your clothing were made of the same material than if you dried different kinds of clothing together? – Tumbling motion produces static charges in dry air – Charge transfer is easier between different materials 2) Good electrical conductors, such as metals, are typically good conductors of heat; electrical insulators, such as wood, are typically poor conductors of heat. Explain why there should be a relationship between electrical conduction and heat conduction in these materials. – Both types of conduction involves free electrons – http://www.doitpoms.ac.uk/tlplib/thermal_electrical/metal_thermal.php 3) If you walk across a nylon rug and then touch a large metal object such as a doorknob, you may get a spark and a shock. Why does this tend to happen more on dry days than on humid days? Why are you less likely to get a shock if you touch a small metal object, such as a paper clip? – Charge builds up easier in dry air, humid air discharges easier – Large objects can accept more electrons Phys272 - Spring 14 - von Doetinchem - 90 Gauß's law ● ● ● Assumption: any distribution of charge surrounded by an imaginary surface: Gauß's law is a relationship between the field at all the points on the surface and the total charge enclosed within the surface. How much charge is inside the imaginary surface? Phys272 - Spring 14 - von Doetinchem - 91 Electric flux and enclosed charge ● ● ● Analogy: positive charges flow out of the surface and negative charges flow into the surface. If there is no enclosed charged: electric field flux going into the surface cancels flux out of the surface. Charges outside the enclosed surface do not give a net electric flux. Phys272 - Spring 14 - von Doetinchem - 92 Electric flux and enclosed charge ● ● Size of the enclosed surface does not matter and only depends on the enclosed charge Enclosing surface can have arbitrary shape. → Gauß's law Phys272 - Spring 14 - von Doetinchem - 93 Calculating electric flux ● Electric flux: we make the analogy of a flowing fluid, BUT electric flux is not actually flowing. ● How to calculate flux? ● How many field lines pass through the area? Phys272 - Spring 14 - von Doetinchem - 94 Flux of an uniform electric field ● Unit vector points outward from a closed surface Phys272 - Spring 14 - von Doetinchem - 95 Electric flux through a disk ● ● Flat surface in a uniform electric field sanity check: the perpendicular value is the highest value Phys272 - Spring 14 - von Doetinchem - 97 Flux of a nonuniform field ● ● General definition of electric flux: If flux is not uniform and area is curved → just integrate over infinitesimal area elements d General electric flux definition Phys272 - Spring 14 - von Doetinchem - 98 Electric flux through a sphere ● ● ● Surface is not flat, electric field not uniform → make smart choice on enclosing surface to simplify the problem, make use of symmetries Electric field is perpendicular to surface Radius cancels out → the flux through any surface enclosing a single point charge is independent of the shape or size of the surface Phys272 - Spring 14 - von Doetinchem - 100