* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download slides
Multiferroics wikipedia , lookup
Superconductivity wikipedia , lookup
Alternating current wikipedia , lookup
Insulator (electricity) wikipedia , lookup
Hall effect wikipedia , lookup
Eddy current wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Maxwell's equations wikipedia , lookup
Electromagnetism wikipedia , lookup
Faraday paradox wikipedia , lookup
Potential energy wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Electrocommunication wikipedia , lookup
History of electrochemistry wikipedia , lookup
Electric machine wikipedia , lookup
Static electricity wikipedia , lookup
Electroactive polymers wikipedia , lookup
Lorentz force wikipedia , lookup
Electrical injury wikipedia , lookup
Electromagnetic field wikipedia , lookup
Electric charge wikipedia , lookup
Electric current wikipedia , lookup
Electromotive force wikipedia , lookup
Physics 272 February 7: Review Spring 2017 http://go.hawaii.edu/j8M Prof. Philip von Doetinchem [email protected] PHYS272 - Spring 17 - von Doetinchem – I/183 Coulomb's law with vectors absolute charge values unit vector along the direct connection between charges q1 and q2 → do not confuse the actual vector and the unit vector of ● ● ● ● distance between charges positive or negative direction comes from product of q1 and q2 Strength of electric force is proportional to 1/r2 The Magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Direction is always along the line of the two charges If both charges are positive: repulsive If both charges are negative: repulsive If have charges have opposite charge signs: attractive PHYS272 - Spring 17 - von Doetinchem – I/184 Superposition of forces ● Total force is the vector sum of forces: principle of superposition of forces: PHYS272 - Spring 17 - von Doetinchem – I/185 Electric field of two point charges ● Electric field strength ● Electric field of two positively charged point charges with the same magnitude of charge Electric field as a function of x,y direction (z=0) electric field strong high potential y direction electric field strong high potential x direction Electric field of a point charge PHYS272 - Spring 17 - von Doetinchem – I/186 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 17 - von Doetinchem – I/187 Electron in a uniform field ● Release of an electron in a uniform electric field ● According to Newton's law: ● Electric potential energy of electron at rest is converted into to kinetic energy: PHYS272 - Spring 17 - von Doetinchem – I/188 Flux of an uniform electric field PHYS272 - Spring 17 - von Doetinchem – I/189 Point charge inside a nonspherical surface ● ● Electric flux is positive (negative) where the electric field points out (into) of the surface Electric field lines can begin or end inside a region of space only when there is charge in that region PHYS272 - Spring 17 - von Doetinchem – I/190 General form of Gauß's law ● ● ● Total electric field is the vector sum of the electric fields of the individual charges inside the enclosed surface General form: The total electric flux through a closed surface is equal to the total (net) electric charge inside the surface, divided by 0. PHYS272 - Spring 17 - von Doetinchem – I/191 Electric potential energy ● ● ● ● Charged particle moving in a field: field exerts work on particle Work can be expressed as potential energy: position of a charge in an electric field Conservative force → required work independent of exact path Potential energy increases if charged particle moves in opposite direction of electric force PHYS272 - Spring 17 - von Doetinchem – I/192 Electric potential ← potential of a point charge ● ● ● Moving with the direction of the electric field means moving in the direction of decreasing potential Moving a charge slowly against an electric field requires an external force, equal and opposite to the electric force. Only the potential difference matters for the strength of the electric field PHYS272 - Spring 17 - von Doetinchem – I/193 Capacitors and capacitance ● ● ● ● Capacitor: just insulate two conductors (with same amount of negative and positive charge) Work must be done to move charges through the resulting potential → stored electric potential energy Electric field is proportional to the stored charge (the same is true for the potential difference) Capacitance stays constant and only depends on the properties of the capacitor and not the operational parameters: ← parallel plate capacitor PHYS272 - Spring 17 - von Doetinchem – I/194 Capacitors in series ● ● ● Charges on all plates have the same magnitude Equivalent capacitance of a series combination of capacitors is always less than any individual capacitance. Charges on plates are the same, but if the dimensions are different → potential for each capacitor different PHYS272 - Spring 17 - von Doetinchem – I/195 Capacitors in parallel ● ● ● ● Charges can reach capacitors independently from the source Imagine one big capacitor that you split into multiple smaller capacitors The parallel combination of capacitors always has a higher capacitance than the individual capacitances Charges are generally not the same on each capacitor PHYS272 - Spring 17 - von Doetinchem – I/196 Electric field energy ● ● Charging a capacitor: work against the electric field between the plates Energy is stored in the field in the region between the plates PHYS272 - Spring 17 - von Doetinchem – I/197 Induced charge and polarization ● When dielectric is inserted and charge is kept constant → potential difference drops → electric field drops → surface charge density drops, but not the charge ● When dielectric is inserted and voltage is kept constant → potential difference is constant → stored energy increases ● ● Redistribution of charges in dielectric occurs: polarization Induced charge: PHYS272 - Spring 17 - von Doetinchem – I/198 Current, drift velocity, current density ● Amount of charge flowing through an area: Current: Current density: ● Current in a conductor is the product of the density of moving charged particles, the magnitude of charge of each such particle, the magnitude of the drift velocity, and the crosssection area PHYS272 - Spring 17 - von Doetinchem – I/199 Resistivity ● ● ● ● Generally current density in conductor depends on electric field and the properties of the material as a function of temperature Ohm's law: Resistivity of a material is the ratio of electric field and current density The greater the resistivity the greater the field has to be to achieve the same current density PHYS272 - Spring 17 - von Doetinchem – I/200 Resistance Potential difference V higher potential lower potential ● ● Resistance Current and potential difference are easier to measure than current density and electric field As current flows through electric potential difference → electric potential energy is lost → energy goes into the ions PHYS272 - Spring 17 - von Doetinchem – I/201 Electromotive force and circuits ● ● Ideal source of emf brings charge to higher potential energy level without increasing the kinetic energy Charge is not used up in a circuit and is not accumulating in the circuit elements. Both sides of the terminal of a battery have the same current for an ideal source of emf. PHYS272 - Spring 17 - von Doetinchem – I/202 Energy and power in electric circuits ● How fast is energy delivered or extracted? ● If a charge passes through a circuit element: → change of potential energy BUT current stays the same → no gain of kinetic energy ● Potential energy change: Power (energy transfer rate) ● Unit: 1J/s=1watt=1W ● Power for a pure resistance (rate of energy transfer into element): PHYS272 - Spring 17 - von Doetinchem – I/203 Formulas provided for the midterm PHYS272 - Spring 17 - von Doetinchem – I/204