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Superposition of Forces

Superposition of Forces. r. r. We find the total force by adding the vector sum of the individual forces.

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Superposition of Forces

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  1. Superposition of Forces r r We find the total force by adding the vector sum of the individual forces.

  2. Work Problem 21-1821-18. (III) Two charges, and are a distance apart. These two charges are free to move but do not because there is a third charge nearby. What must be the magnitude of the third charge and its placement in order for the first two to be in equilibrium?

  3. Electric Field of a Point Charge

  4. Relation between F and E Don’t confuse this charge q1 with the test charge q0 or the original charges q that produced E. The test charge q0 was used to find the electric field. This is a real charge q1 placed in the electric field.

  5. Electric Field Lines for a Point Charge

  6. Electric Field Lines for Systems of Charges We call this a dipole. It is a dipole field.

  7. The Electric Field of a Charged Plate

  8. A Parallel-Plate Capacitor

  9. The electric field near a conducting surface must be perpendicular to the surface when in equilibrium.

  10. Conductor placed around a charge +Q

  11. 21-86. An electron moves in a circle of radius r around a very long uniformly charged wire in a vacuum chamber, as shown in the figure. The charge density on the wire is λ = 0.14 μC/m. (a) What is the electric field at the electron (magnitude and direction in terms of r and λ? (b) What is the speed of the electron?

  12. We can work all kinds of problems with charged particles moving in electric fields. Electron entering charged parallel plates

  13. Electric flux: Electric flux through an area is proportional to the total number of field lines crossing the area.

  14. Flux through a closed surface: positive negative

  15. The net number of field lines through the surface is proportional to the charge enclosed, and also to the flux, giving Gauss’s law: This can be used to find the electric field in situations with a high degree of symmetry.

  16. Electric field of charged sheet

  17. Electric Potential V definition!! Electric potential, or potential, is one of the most useful concepts in electromagnetism. This is a biggie!!

  18. Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative – potential energy can be defined. Change in electric potential energy is negative of work done by electric force:

  19. The Potentials of Charge Distributions If the electric field is known: For one point charge: For many point charges:

  20. The Potentials of Charge Distributions If the electric field is known: For differential charge: For many point charges: For a continuous charge distribution:

  21. Equipotential Surfaces An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential.

  22. Equipotential Surfaces Another case showing electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. We can also see that equipotentials are perpendicular to electric fields from the equation

  23. Equipotential Surfaces Equipotential surfaces are always perpendicular to field lines; they are always closed surfaces (unlike field lines, which begin and end on charges). Electric field and equipotentials for electric dipole.

  24. 23-74. Four point charges are located at the corners of a square that is 8.0 cm on a side. The charges, going in rotation around the square, are Q, 2Q, -3Q and 2Q, where Q = 3.1 μC. What is the total electric potential energy stored in the system, relative to U = 0 at infinite separation?

  25. When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: The quantity C is called the capacitance.

  26. Parallel plate capacitor The capacitance value depends only on geometry!

  27. Capacitors in Parallel Capacitors in parallel have the same voltage across each one. The equivalent capacitor is one that stores the same charge when connected to the same battery:

  28. Capacitors in Series Capacitors in series have the same charge. In this case, the equivalent capacitor has the same charge across the total voltage drop. Note that the formula is for the inverse of the capacitance and not the capacitance itself!

  29. Effect of a Dielectric on the Electric Field of a Capacitor

  30. A dielectric is an insulator, and is characterized by a dielectric constant . Capacitance of a parallel-plate capacitor filled with dielectric: Using the dielectric constant, we define the permittivity:

  31. Energy in electric field The energy U in a capacitor is The volume is Ad, and the energy density u is

  32. Defibrillator

  33. Potential energy of a charged capacitor: All three expressions are equivalent!

  34. A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit! Open circuit

  35. Direction of Current and Electron Flow

  36. Resistors are color coded to indicate the value of their resistance.

  37. Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: The constant ρ, the resistivity, is characteristic of the material.

  38. Energy and Power The unit of electrical power is watt W (J/s). If we use Ohm’s law with this equation, we have

  39. AC Voltage and Current for a Resistor Circuit Note that I and V are in phase!!

  40. 25-36. (II) A 120-V hair dryer has two settings: 850 W and 1250 W. (a) At which setting do you expect the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting; and (c) the higher setting.

  41. 25-43. (II) How many 75-W lightbulbs, connected to 120 V as in Fig. 25–20, can be used without blowing a 15-A fuse?

  42. Resistors in Series Current is not used up in each resistor. Same current I passes through each resistor in series.

  43. A parallel connection splits the current; the voltage across each resistor is the same:

  44. Analyzing a Complex Circuit of Resistors

  45. Kirchhoff’s Junction Rule In + Out - The sum of currents meeting at a junction must be zero. I1 – I2 – I3 = 0 or I1= I2 + I3

  46. Kirchhoff’s Loop Rule The sum of potential differences around any closed circuit loop is zero. Our rules: When going from – to + across an emf the V is +. (+ to -, it is -). 2) When going across resistor in direction of assumedI, the V is -. (Opposite, it is +).

  47. Measuring the Current in a Circuit We want ammeter to have very low resistance so it will not affect circuit. Ammeters go in series.

  48. Measuring the Voltage in a Circuit We want voltmeter to have very large resistance so it will not affect circuit. Voltmeters go in parallel across what is being measured.

  49. An ohmmeter measures resistance; it requires a battery to provide a current. These circuits are much more complicated. Rsh is a shunt resistor to change scales. Rser is a resistor to adjust galvanometer scale zero.

  50. Magnetic Field Lines for a Bar Magnet Imagine using a test pole N; place it at any point and see where the force is. Just like we do for electric fields. We actually use small compasses to do this.

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