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Understanding Electrical Potential Energy in Physics

Learn about electrical potential energy (PE) in the context of physics, its relationship to electric fields, work done by charges, and potential difference between charges. Explore concepts like PE calculations and unit analysis, alongside practical applications in a uniform electric field.

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Understanding Electrical Potential Energy in Physics

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  1. Electrical Energy & Current Honors Physics

  2. Electrical Potential Energy • PE associated with a charge due to its position in an electric field. • Analogous to PEg • PEg of an object results from its position in a gravitational field (mgh) • Is a component of mechanical energy • ME = KE + PEgrav + PEelastic + PEelectric

  3. Gravitational Potential Energy Physicsclassroom.com

  4. Similarity of PEelectric and PEg • PEg = mgh • m is mass • g is gravitational field (ag) • h is distance above a reference point • PEelect = -qEd • q is charge • E is electric field strength • d is component of displacement in the direction of the electric field from reference point • Using dimensional analysis, what is the unit of PEelect?

  5. Electric Potential Energy & Work Physicsclassroom.com

  6. Electric Potential Energy & Work Physicsclassroom.com

  7. Electric Work • Whenever a force moves an object, work is done on the object. • When an electric force moves a charge, work is done on that charge. • It is the electric field, E, that exerts force on a charge • Therefore, the electric field, E, does work on a charge. • This results in a change in PEelect.

  8. Electric PE in a Uniform Electric Field • A uniform field is one that has the same magnitude and direction at all points, such as between two parallel plates • Remember: electric field lines are always directed from away from positive and toward negative

  9. Electric Potential Energy • Recall that ΔPE = -W • When charge q is released at point a, electric force will move the charge to b, i.e. • The electric field does work on the charge q • So, the PE of charge a decreases

  10. Electric Potential Energy • W = Fd • Since F = qE (remember E = F/q) • W = qEd • PEb-PEa= -qEd • ΔPE = -qEd • Significance of the (-) sign: PEelect • Increases if charge is (-) • Decreases if charge is (+)

  11. PE as a charge moves in a uniform electric field ΔPE = -qEd Negative sign indicates that PE will increase if the charge is negative and decrease if the charge is positive

  12. Potential Energy between two charges

  13. Learning check • When a negative charge moves in the direction of an electric field it gains PE (T/F). • When a positive charge moves against the electric field it loses PE (T/F) • In order for a negative charge to lose PE, it must move (with/against) the electric field. • The change in PE of a charge is equal to –qEd (T/F)

  14. Potential Difference • Electric potential (V) is the ratio of PEelect to charge q • Represents the work needed to move a charge against electric forces from a reference point to some other point in an electric field, divided by the charge • W = Fd = qEd • The SI units of electric potential are what? Which is a …?

  15. Potential difference • The change in electric potential • The difference in electrical potential between two points • Is the work that must be done against electric forces to move a charge from one point to another divided by the charge • Is the change in energy per unit charge

  16. Potential Difference • Unit is the volt (V) • Remember: • PEelect is a quantity of energy • Electrical potential is a measure of energy per unit charge • Potential difference describes change in energy per unit charge

  17. Potential Difference in a Uniform Electric Field • Varies in a uniform field with displacement from a reference point • Where d is displacement parallelto the field • Use this equation to determine potential difference between two points in a field

  18. Potential Difference at a Point Near a Charge • One point is near the charge • The other point is at infinity

  19. Sample Problem • As a charge moves xa = 4.0 cm to xb = 6.0 cm in a uniform field of 350 N/C, it loses 4.5 x 10-16 J of potential energy. • What is the magnitude of the charge? • 3.2 x 10-17C • What is the potential difference between the two points a and b? • -14.0V

  20. Electric potential due to multiple charges • Electric potentials are scalar quantities (whew!) • So…. • Total potential at some point in a field is the simple sum of the potentials due to each charge • Keep track of signs!

  21. Summary of Formulas ΔPE = -qEd

  22. 17.2 Capacitance • Capacitors are devices that store electrical PE • Often constructed of parallel metal plates • When connected to a battery, the plates become charged • When fully charged, ∆Vcap = ∆Vbat

  23. Schematic Representation of a Capacitor and Battery Intro to Capacitor

  24. Construction of a Capacitor • Parallel plates • Parallel plates separated by an insulator (dielectric material) rolled into a cylinder saves space

  25. Capacitance • Ability of a conductor to store energy in the form of separated charges • Unit of capacitance is the Farad, named for Michael Faraday • 1F = 1C/V • 1 Farad is a large amount of capacitance so… • Often use pF, nF, or µF • Supplemental instruction on capacitance • View on your own, ~ 17 min.

  26. Capacitance of a Parallel-Plate Capacitor in a Vacuum • When no material exists between the plates • ε0 is the permittivity of the medium between the plates • A measure of ability to develop an electrical field, permitting transfer of charges • ε0 in a vaccuum is 8.85 x 10-12 C2/Nm2

  27. Dielectric Materials • Materials placed between the plates of a capacitor can increase capacitance. • Typically these are insulating materials

  28. Dielectric Constants (K) • Dielectric materials have different values of “dielectric constant” (K). • Increase capacitance

  29. Performance of Dielectric Materials • Molecules of the dielectric are polarizable • As charge builds on the capacitor plates, dielectric molecules orient to the electric field • This effectively reduces the charge on the plates…. • allowing more charge to be carried by each plate

  30. Capacitor Discharge • The opposite of charging, releasing stored charge • Electrical potential of the capacitor is used to do electrical work such as … • The flash of a camera • Signaling the stroke of a computer keyboard

  31. Capacitance of a Sphere • R is radius • Because the earth has a large radius, it has a very large capacitance • i.e., the earth can accept or supply a very large amount of charge without changing its electrical potential • This is why the earth is “ground,” (reference point for measuring potential differences)

  32. Energy and Capacitors • Because work is done to move charges to and from opposite plates… • A charged capacitor holds electrical potential energy • PE stored in a charged capacitor is equal to the (–) work done to charge it

  33. Breakdown voltage • Voltage at which discharge begins, i.e. charges move

  34. Energy and Capacitors PE Stored in a Charged Capacitor

  35. Current and Resistance Current is the rate of movement of charge Rate of movement of electrons through a cross-sectional area

  36. Sample Problem If current flowing through a light bulb is 0.835 A, how long does it take for 1.67 C of charge to pass through the filament of the bulb? 2.00 seconds

  37. Conventional Direction of Current • Depending upon the circumstances, either positive, negative, or both can move. • Particles that move are called charge carriers • By convention, direction of current is defined as the direction a positive charge moves or would move if it could. • In metals, only electrons can move. • Good conductors permit charge carriers to move easily • Electrons in metals • Ions in solution (electrolytes)

  38. Conventional Direction of Current

  39. Drift Velocity • Recall the structure of metals • Valence electrons move about randomly due to their thermal energy • Their net movement is zero • But if an electric field is established in the wire, there is a net movement of electrons against the electric field (toward +) • Drift velocity animation (for enrichment) http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif

  40. Drift Velocity Consider motion of an electron through a wire It is the electric field that exerts force and thereby sets charge carriers in motion (E = F/Q) E propagates very rapidly (near speed of light) Charge carriers move more slowly, in an erratic path, Called drift velocity Slow: e.g. in a copper wire carrying a 10.0 A current, vdrift = 0.246 mm/s

  41. Relationship of Voltage and Current: Conductance and Resistance http://s3.amazonaws.com/answer-board-image/c8b9a2d5-43d2-40b4-a578-1874d002386f.gif

  42. Resistance to Current Opposition to electric current Unit of electrical resistance is the ohm (Ω) More commonly known as Ohm’s law

  43. Ohmic and Non-ohmic Materials Materials which follow ohm’s law are ohmic materials Resistance is constant over a wide range of potential differences (linear) Non-ohmic materials have variable resistance (non-linear) Diodes are constructed of non-ohmic materials

  44. Other Factors Affecting Resistance

  45. Function of Resistance • From Ohm’s Law, changing resistance can change current • So, if current needs to be reduced in a circuit, you can increase the resistance • In many cases, ∆V is constant, so changing resistance is the only option for reducing current.

  46. Electrical Resistance in the Body • Electrical resistance is reduced as the body becomes wet or sweats • This is due to the greater availability of ions to conduct current • Practical applications: • Your body is more susceptible increased current when wet • Lie detectors • EKGs, etc

  47. Potentiometers • Devices that have variable resistance • “Pots” • Applications • Control knobs on electronic devices • Stereos, dimmer switches, joy sticks, etc.

  48. 17.4 Electric Power • A potential difference (∆V) is necessary to cause current (I) • Batteries supply chemical energy (PEchem) which can be converted into PEelect • Generators convert mechanical energy into electrical Peelect • E.g. hydroelectric power plants • Wind turbines • Coal or natural gas power plants • Nuclear power plants • Solar power • Geothermal energy

  49. Direct and Alternating Current • DC current flows in one direction only • Electrons move toward the (+) terminal • Conventional current directed from (+) to (-) • AC current • Terminals of source of ΔV constantly switch • Causing constant reversal of current, e.g. 60 Hz • Rapid switching causes e-s to vibrate rather than have a net motion.

  50. DC and AC • DC • constant • uni-directional • AC • not constant • bi-directional

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