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Physics 272 February 4 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 - 179 Undergraduate Research Opportunities ● ● ● ● ● Now is the time to consider applying for funding to bring your ideas for research and creative projects to fruition! Research and travel awards are given for up to $5,000 for individuals and $10,000 for groups. Undergraduate students from all academic disciplines are encouraged to apply. Electronic funding applications will be accepted from eligible undergraduate students from February 2, 2014 until March 3, 2014 at 11:59 pm. To learn more about UROP visit our website at: http://manoa.hawaii.edu/urop/ Phys272 - Spring 14 - von Doetinchem - 180 Electric potential energy in an uniform field ● ● Potential energy decreases if a charged particle moves in the direction of the electric field If the displacement of a positive charge is in the direction of the electric field the work is positive Phys272 - Spring 14 - von Doetinchem - 182 Electric potential ● ● Describe potential energy on a “per unit charge” basis (like the electric field describes force per unit charge) Determination of electric field is often easier by using the potential Source: http://de.wikipedia.org/wiki/Alessandro_Volta Alessandro Volta 1745-1825 ● Potential energy and potential are scalars ● Potential difference in circuits is often called voltage Phys272 - Spring 14 - von Doetinchem - 187 Calculating electric potential ● ● ● Potential of a continuous charge distribution: Potential is zero at points that are infinitely far away from all the charges creating the potential Electric potential at a certain point is the potential energy that would be associated with a unit charge placed at that point. Phys272 - Spring 14 - von Doetinchem - 188 Equipotential surfaces ● ● ● Equipotential lines are similar to field lines → they help us to visualize a potential Similar to a topographic map: line corresponds to same potential Electric field lines Equipotential lines Charge can be moved Source: http://de.wikipedia.org/wiki/%C3%84quipotentialfl%C3%A4che around this potential line without exerting electric force → force must be perpendicular to equipotential line → field lines are perpendicular to potential lines ● Lines are closer to each other for steeper gradients ● Equipotential lines cannot intersect ● Electric field is generally not constant over an equipotential line Phys272 - Spring 14 - von Doetinchem - 192 Potential gradient Phys272 - Spring 14 - von Doetinchem - 194 Potential gradient ● Vector electric field can be calculated from scalar electric potential ● Potential gradient points towards the most rapid change in position. ● ● The shortest way to the next equipotential line is perpendicular to the old line: → electric field perpendicular to equipotential lines Absolute value of potential is not important for electric field, only the local change. Phys272 - Spring 14 - von Doetinchem - 195 Electric potential energy and electric potential ● ● ● ● Electric potential energy: – Electric force is conservative – Work done by an electric force is represented by the change in potential energy Electric potential: – Potential energy per unit charge – Potential difference between two points equals the amount of work to move a test charge between those points. – Potential difference between two points is given by the line integral along the electric field Equipotential lines are lines of constant potential. Electric field lines and equipotential lines are perpendicular. The electric field can be calculated from the potential gradient of the electric potential. Phys272 - Spring 14 - von Doetinchem - 198 Capacitance and dielectrics ● ● ● ● ● ● ● Capacitor stores electric potential and electric charge 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 Applications: flashs, electronic devices Capacitor has a certain capacitance depending on its properties: size, shape, material Capacitance increases when using an insulating material between the negative and positive side (polarization) Electric field can be seen as a store-house of electric potential energy Phys272 - Spring 14 - von Doetinchem - 199 Capacitors and capacitance ● ● ● ● ● Charging capacitor: conductors initially uncharged Transfer electrons from one side to the other Net charge on capacitor is zero Common way of charging: connect sides to different terminals of a battery Electric field is proportional to the stored charge (the same is true for the potential difference) ● Capacitance stays constant: ● Capacitance is a measure of the ability of a capacitor to store energy. Phys272 - Spring 14 - von Doetinchem - 200 Calculating capactiance: capacitors in vacuum ● ● ● Nothing between oppositely charged conductors condenser microphone: capacitance changes due to flexible plate moved by sound waves → current flow One farad is a very large amount: typical values: – flash unit in a camera: microfarad (µF, 10-6) – radio tuning unit: 10-100 picofarad (pF, 10 -12) Phys272 - Spring 14 - von Doetinchem - 202 Spherical capacitor ● Outer sphere makes no contribution to the field between the sphere Phys272 - Spring 14 - von Doetinchem - 204 Cylindrical capacitor ● Important property of parallel-plate, spherical, an cylindrical capacitors: capacitance just depends on dimensions Phys272 - Spring 14 - von Doetinchem - 205 Capacitors in series ● ● ● ● ● Combining capacities helps you to get the capacitance you need for your application Series connection: capacitors are connected one after the other 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 14 - von Doetinchem - 208 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 14 - von Doetinchem - 209 Equivalent capacitance ● Make a drawing of the arrangement ● Identify groups of parallel and series connections ● ● Series connection: capacitors have same charge, different potential difference Parallel connection: same potential difference, different charge Phys272 - Spring 14 - von Doetinchem - 210 Capacitor network Phys272 - Spring 14 - von Doetinchem - 211