Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Gibbs free energy wikipedia , lookup
Electromagnetism wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Anti-gravity wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Work (physics) wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Lorentz force wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Potential energy wikipedia , lookup
Electric Potential Energy Work is defined as the product of displacement d and a parallel applied force F. Work = Fd; Units: 1 J = 1 N m Potential Energy U is defined as the ability to do work by virtue of position or condition. (Joules) Kinetic Energy K is defined as the ability to do work by virtue of motion (velocity). (Also in Joules) Work (Fd) is positive if an applied force F is in the same direction as the displacement d. B F m mg A d Consider work against g to move m from A to B, a vertical height h. Work = Fh = mgh At level B, the potential energy U is: U = mgh (gravitational) B F m mg h g A The external force does positive work; the gravity g does negative work. The external force F against the g-field increases the potential energy. If released, the field does work. An external force F moves +q from A to B against the field force qE. Work = Fd = (qE)d At level B, the potential energy U is: U = qEd (Electrical) The E-field does negative work; External force does positive work. B ++++ Fe +q + d qE E A - - - - The external force F against the E-field increases the potential energy. If released, the field does work. Suppose a negative charge –q is moved against E from A to B. Work by E = qEd At A, the potential energy U is: U = qEd (Electrical) No external force is required ! B ++++ F=qE -q d E A - - - - The E-field does positive work on –q decreasing the potential energy. If released from B nothing happens. Equation for Work in a Uniform Electric Field The work W done by the electric field E to move the charge a distance d (in a uniform electric field) is W = Fd = qEd where F = qE, since E = F/q Work = -ΔPE The electrostatic force is conservative – potential energy can be defined. Change in electric potential energy is negative of work done by electric force: ΔPE = U = Where d is the distance between charged plates What about a Non-Uniform Field? Electric PE for a point charge (relative to some source point charge) Or, PE Between Two Charges. Δ P.E. = W = F d = F r = ΔP.E. = U = r = (as measured from infinity) Note: A reference point of PE = 0 is conventionally set at infinity because at this location, the electrical force on a charged particle due to a source charge would be zero. A • 8 cm +2 nC +Q +6 µC U = 1.35 mJ Positive potential energy A • • B 12 cm 8 cm Questions: If +2 nC moves from A to B, does field E do + or – work? Does P.E. increase or decrease? +Q • C 4 cm +6 µC Moving positive q +2 nC If +2 nC moves from A to C (closer to +Q)… the field E does negative work and P.E. increases. A • • B 12 cm 8 cm From Ex-1: UA = + 1.35 mJ ΔU = UB – UA = 0.9 mJ – 1.35 mJ +Q +6 µC ΔU = -0.450 mJ Note that P.E. has decreased as work is done by E. A • • B 12 cm 8 cm Questions: If -q moves from A to B, does field E do + or – work? Does P.E. increase or decrease? +Q • C 4 cm +6 µC Moving negative q - What happens if we move a –2 nC charge from A to B instead of a +2 nC charge. This example follows . . . A • From Ex-1: UA = -1.35 mJ 8 cm • B 12 cm +Q +6 µC 2 Nm (9 × 10 9 2 )(6 × 10 −6 C)(−2 × 10 −9 C) C UB = = −0.900mJ 0.12m UB – UA = -0.9 mJ – (-1.35 mJ) ΔU = +0.450 mJ € A – charge moved away from a + charge gains P.E. Example 4: Electric Potential Energy Two alpha particles (helium nuclei), each consisting of two protons and two neutrons, have an electrical potential energy of 6.32 x 10-19 J. What is the distance between these particles? PE = 6.32x10-19 J ; q1 = q2 = +2e = 3.2x10-19 C ; PE = k (q1q2)/ r k (q1q2) / PE = r (8.99x109)(3.2x10-19)(3.2x10-19) r = 1.46 x 10-9 m / (6.32x10-19) = r r=? Electric Field . E r ++ + + ++Q++ E is a Vector An electric field is a property of space allowing prediction of the force on a charge at that point. The field E exists independently of the charge q and is found from: P. r + ++ + ++Q++ Potential U = qV = (-2 x 10-9C)(400 J/C); U = -800 nJ Analogy between gravitational and electrical potential energy: Analogy between gravitational and electrical potential energy: Electrical potential energy depends on charge, but electrical potential does not. A potential of one volt at a given point means that a charge of one coulomb placed at that point will experience a potential energy of one joule. P. r + ++ + ++Q++ Potential The potential due to a positive charge is positive; The potential due to a negative charge is negative. (Use sign of charge.) Analogy between gravitational and electrical potential energy: Analogy between gravitational and electrical potential energy: Electrical potential energy depends on charge, but electrical potential does not. Electrostatic Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge: kQ = r Unit of electric potential: the volt (V). € 1 V = 1 J/C. Electric Potential vs Electric Potential Energy • Which charge has more electric potential? • Which has more electric potential energy? Electric Potential vs Electric Potential Energy • Electric Potential (voltage) is independent of charge (it is energy per charge) • Electric Potential Energy is charge dependent P. r 6 cm -- -Q- -- - Negative V at Point P : VP = -750 V Q = -5 nC U = 3.00 mJ Since P.E. is positive, E will do + work if q is released. The Electric Potential V in the vicinity of a number of charges is equal to the algebraic sum of the potentials due to each charge. Q1 - r1 r3 Q3 - • A r2 + Q2 Potential is + or – based on sign of the charges Q. B • 2 cm Q1 + +3 nC 6 cm A • 2 cm VA = 450 V – 2250 V; VA = -1800 V Q2 = -5 nC B • 2 cm Q1 + +3 nC 6 cm A • 2 cm VB = 1350 V – 450 V; VB = +900 V Q2 = -5 nC Potential Difference: ΔV =VAB = VB - VA WorkAB (Work BY E-field) = -qΔV The positive and negative signs of the charges may be used mathematically to give appropriate signs. B • VA = -1800 V VB = +900 V 2 cm Q1 + +3 nC 6 cm A • VAB = +2700 V Q2 2 cm - -5 nC Work = -5.40 mJ Thus, an external force was required to move the charge. VA = -1800 V VB = +900 V B • 2 cm Q1 + +3 nC 6 cm A • VBA = -2700 V Q2 - Work = +5.40 mJ The work is done BY the E-field this time ! 2 cm -5 nC VA + + + + Constant E field: F = qE +q F = qE VB - - - VAB = -Ed The potential difference between two oppositely charged parallel plates is the product of E and d. E VA + + + + E +q F = qE VB - - - - - U V = →U = Vq q - U = −qEd € The E-field expressed in volts per meter (V/m) is € and is equivalent to known as the potential gradient the N/C. The volt per meter is the better unit for current electricity, the N/C is better electrostatics. Example 8: Electric Potential Energy A charge moves a distance of 2.0 cm in the direction of a uniform electric field having a magnitude of 215 N/C. The electrical potential energy of the charge decreases by 6.9x10-19 J as it moves. Find the magnitude of the charge on the moving particle. ΔPE = -6.9x10-19J ; d = 2cm = 0.02m ; ΔPE = -qEd - ΔPE / Ed = q - (-6.9x10-19J) / ((215)(0.02)) = q 1.6 x 10-19 C = q E = 215 N/C ; q=? Electric Potential Energy and Potential Electric Potential Near Multiple charges: WorkAB = q(VA – VB) Oppositely Charged Parallel Plates: Work BY E-field Work done on charge (by external force)? Yes Electric PE is greatest at: A Electric potential is greatest at: or B A or B or No Work done on charge (by external force)? Yes Electric PE is greatest at: A Electric potential is greatest at: or B A or B or No Work done on charge to get from A to B? Yes or No Electric PE is greatest at: A Electric potential is greatest at: or B A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B What if the test charge were negative? Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Potential due to an electric field is assumed, by definition, to originate from a positive source charge (field lines go out from positive to negative). An electron moving to a higher potential (closer to the field line origins) will be losing potential energy. So ΔPE is negative, and, since q is also negative (in ΔV = ΔPE / q), ΔV is positive, moving from A to B. The opposite will hold if it is being moved closer to a like (negative) charge. In that case it will be moving along the direction of the electric field lines. Also, it helps if you think of electric potential as a property of the field, but think of PE as a property of the charge. Read more in our book, p.572 Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Work done on charge? Yes or No Electric PE is greatest at: or B A Electric potential is greatest at: A or B Potential Difference • Batteries provide potential difference between one end of the circuit and the other Potential Difference • Batteries provide potential difference between one end of the circuit and the other • Positive charges flow from high to low electric potential The terminals of a battery are defined as follows: Potential Difference • Batteries provide potential difference between one end of the circuit and the other • Positive charges flow from high to low electric potential Potential Difference • Batteries provide potential difference between one end of the circuit and the other • Positive charges flow from high to low electric potential • Negative charges flow from _____ to _____ electric potential. Potential Difference • Batteries provide potential difference between one end of the circuit and the other • Positive charges flow from high to low electric potential • Negative charges flow low to _____ high from _____ electric potential. The diagram shows a light bulb connected to a 12-V car battery. The + and - terminals are shown. a. As a + charge moves through the battery gains (gains, loses) from D to A, it ________ potential energy and ________ (gains, loses) electric potential. The point of highest energy within a battery is the ______ (+, -) terminal. b. As a + charge moves through the external circuit from A to D, it ________ (gains, loses) potential energy and ________ (gains, loses) electric potential. The point of highest energy within the external circuit is closest to the ______ (+, -) terminal. VA = VB > VC = VD c. Use >, <, and = signs to compare the electric potential (V) at the four points of the circuit. The diagram shows a light bulb connected to a 12-V car battery. The + and - terminals are shown. a. As a (-) charge moves through the battery from A to D, it ________ (gains, loses) potential energy and ________ (gains, loses) electric potential. The point of highest energy within a battery is the ______ (+, -) terminal. b. As a (-) charge moves through the external circuit from D to A, it ________ (gains, loses) potential energy and ________ (gains, loses) electric potential. The point of highest energy within the external circuit is closest to the ______ (+, -) terminal. VA = VB > VC = VD c. Use >, <, and = signs to compare the electric potential (V) at the four points of the circuit. Equipotential Lines 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. Equipotential Lines The Electron Volt, a Unit of Energy One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt. The Electron Volt, a Unit of Energy (Another Approach) One electron volt (eV) is the amount of energy experienced by an electron (or proton) when it drops its potential by 1 V. 1eV = ΔPEe = qeΔV = (1.6 x 10-19C) (1V)