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Chapter 16

Chapter 16. Electric Energy and Capacitance. PE is the energy associated with the position of an object within a system relative to some reference point. PE is defined for a system rather than an individual object. PE can also be used to do work or be converted to KE.

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Chapter 16

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  1. Chapter 16 Electric Energy and Capacitance

  2. PE is the energy associated with the position of an object within a system relative to some reference point. • PE is defined for a system rather than an individual object. • PE can also be used to do work or be converted to KE. • Conservation of energy • W = ∆KE • W = -∆PE (PEo – PEf) Review of Potential Energy

  3. The electrostatic force is a conservative force. • Work done by the force is path independent. • It is possible to define an electrical potential energy function with this force. • This PE shares the same characteristics as other PE. • Work done by a conservative force is equal to the negative of the change in potential energy. • W = -∆PE Electric Potential Energy

  4. Work and Electric Potential Energy

  5. Uniform Electric Field • Two metal plates possessing charges equal in size but opposite in charge.

  6. The potential difference (∆V) between two points A and B is defined as the change in the potential energy (final value minus initial value) of a charge q moved from A to B divided by the size of the charge. • ΔV = VB – VA = ΔPE / q Potential Difference

  7. Another way to relate the energy and the potential difference: • ΔPE = q ΔV • Both electric potential energy and potential difference are scalar quantities. • Units of potential difference: volts • V = J/C • A special case occurs when there is a uniform electric field: • DV = VB – VA= -Ed • Gives more information about units: N/C = V/m Potential Difference

  8. Potential difference is notthe same as potential energy. • Electric potential is characteristic of the field only. • Independent of any test charge that may be placed in the field. • Electric potential energy is characteristic of the charge-field system. • Due to an interaction between the field and the charge placed in the field. Potential Energy vs. Potential Difference

  9. A positive charge gains electrical potential energy when it is moved in a direction opposite the electric field. • If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy. • As it gains kinetic energy, it loses an equal amount of electrical potential energy. • A negative charge loses electrical potential energy when it moves in the direction opposite the electric field. Energy and Charge Movements

  10. Energy and Charge Movements • When the electric field is directed downward, point B is at a lower potential than point A. • A positive test charge that moves from A to B loses electric potential energy. • It will gain the same amount of kinetic energy as it loses in potential energy.

  11. When a positive charge is placed in an electric field: • It moves in the direction of the field. • It moves from a point of higher potential to a point of lower potential. • Its electrical potential energy decreases. • Its kinetic energy increases. Summary of Positive Charge Movements and Energy

  12. When a negative charge is placed in an electric field: • It moves opposite to the direction of the field. • It moves from a point of lower potential to a point of higher potential. • Its electrical potential energy increases. • Its kinetic energy increases. • Work has to be done on the charge for it to move from point A to point B. Summary of Negative Charge Movements and Energy

  13. A 12-V battery is connected between two parallel metal plates separated by 0.030 m. Find the magnitude of the electric field. Sample Problem

  14. The point of zero electric potential is taken to be at an infinite distance from the charge. • The potential created by a point charge q at any distance r from the charge is: • A potential exists at some point in space whether or not there is a test charge at that point. Electric Potential of a Point Charge

  15. Electric Field and Electric Potential Depend on Distance • The electric field is proportional to 1/r2. • The electric potential is proportional to 1/r.

  16. Superposition principle also applies. • Key difference: • The total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges. • The algebraic sum is used because potentials are scalar quantities. Electric Potential of Multiple Point Charges

  17. Electrical Potential Energy of Two Charges • V1 is the electric potential due to q1 at some point P. • The work required to bring q2 from infinity to P without acceleration is q2V1. • This work is equal to the potential energy of the two particle system:

  18. If the charges have the same sign, PE is positive. • Positive work must be done to force the two charges near one another. • The like charges would repel. • If the charges have opposite signs, PE is negative. • The force would be attractive. • Work must be done to hold back the unlike charges from accelerating as they are brought close together. Notes About Electric Potential Energy of Two Charges

  19. A 5.0 µC point charge is at the origin, and a point charge q2 = -2.0 µC is on the x-axis at (3.0,0) m, as in the figure. If the electric potential is taken to be zero at infinity, find the total electric potential due to these charges at point P, with coordinates (0, 4.0) m. Sample Problem

  20. Since W = -q(VB – VA), no work is required to move a charge between two points that are at the same electric potential. • W = 0 when VA = VB • All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential. • Therefore, all points on the surface of a charged conductor in electrostatic equilibrium are at the same potential. Potentials and Charged Conductors

  21. Conductors in Equilibrium • The conductor has an excess of positive charge. • All of the charge resides at the surface. • E = 0 inside the conductor. • The electric field just outside the conductor is perpendicular to the surface. • The potential is a constant everywhere on the surface of the conductor. • The potential everywhere inside the conductor is constant and equal to its value at the surface.

  22. The electron volt (eV) is defined as the energy that an electron gains when accelerated through a potential difference of 1 V. • Electrons in normal atoms have energies of 10’s of eV. • Excited electrons have energies of 1000’s of eV. • High energy gamma rays have energies of millions of eV. • 1 eV = 1.6 x 10-19 J The Electron Volt

  23. Equipotentials and Electric Fields Lines – Positive Charge • The equipotentials for a point charge are a family of spheres centered on the point charge. • The field lines are perpendicular to the electric potential at all points.

  24. Equipotentials and Electric Fields Lines – Dipole • Equipotential lines are shown in blue. • Electric field lines are shown in gold. • The field lines are perpendicular to the equipotential lines at all points.

  25. A capacitor is a device used in a variety of electric circuits. • The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates). Capacitance

  26. Units: Farad (F) • 1 F = 1 C / V • A Farad is very large • Often will see µF or pF • V is the potential difference across a circuit element or device. • Q is the magnitude of the charge on either conductor/plate. Capacitance

  27. The capacitance of a device depends on the geometric arrangement of the conductors. • For a parallel-plate capacitor whose plates are separated by air: Parallel-Plate Capacitor

  28. Parallel-Plate Capacitor • The capacitor consists of two parallel plates. • Each have area A. • They are separated by a distance d. • The plates carry equal and opposite charges. • When connected to the battery, charge is pulled off one plate and transferred to the other plate. • The transfer stops when DVcap = Dvbattery.

  29. A parallel plate capacitor has an area of A = 2.00 cm2 (2.00x104 m2) and a plate separation of d=1.00 mm. Find the capacitance. Sample Problem

  30. A circuit is a collection of objects usually containing a source of electrical energy (such as a battery) connected to elements that convert electrical energy to other forms. • These objects can be placed in series or in parallel arrangements. • The equivalent capacitance and the equivalent potential difference can be determined in each case. • A circuit diagram can be used to show the path of the real circuit. Capacitors in Circuits

  31. Capacitors in Parallel • The total charge is equal to the sum of the charges on the capacitors. • Qtotal = Q1 + Q2 • The potential difference across the capacitors is the same. • And each is equal to the voltage of the battery. • ∆V = ∆V1 = ∆V2

  32. More About Capacitors in Parallel • The capacitors can be replaced with one capacitor with a capacitance of Ceq. • The equivalent capacitor must have exactly the same external effect on the circuit as the original capacitors. • Ceq = C1 + C2 + … • The equivalent capacitance of a parallel combination of capacitors is greater than any of the individual capacitors.

  33. Determine the capacitance of the single capacitor that is equivalent to the parallel combination of capacitors shown in the figure and the charge on the 12.0 µF capacitor. Sample Problem

  34. Capacitors in Series • When in series, the capacitors are connected end-to-end. • The magnitude of the charge must be the same on all the plates. • Qeq = Q1 = Q2

  35. More About Capacitors in Series • An equivalent capacitor (Ceq)can be found that performs the same function as the series combination. • The potential differences add up to the battery voltage. • ∆V = ∆V1 + ∆V2 + …

  36. Four capacitors are connected in series with a battery, as in the figure. (a) Find the capacitance of the equivalent capacitor. (b) Find the charge on the 12 µF capacitor. Sample Problem

  37. Capacitor Combinations: A Summary

  38. Find the equivalent capacitance between a and b for the combination of capacitors shown in the figure. All capacitors are in µF. Sample Problem

  39. Consider the combination of capacitors in the figure below. (a) What is the equivalent capacitance of the group? (b) Determine the charge on each capacitor. Sample Problem

  40. Find the charge on each of the capacitors in the figure below. Sample Problem

  41. A dielectric is an insulating material that, when placed between the plates of a capacitor, increases the capacitance. • Dielectrics include rubber, plastic, or waxed paper. • The capacitance is multiplied by the factor κ when the dielectric completely fills the region between the plates. Capacitors with Dielectrics

  42. Capacitors with Dielectrics

  43. Chapter 16 Electric Energy and Capacitance THE END

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