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Summary Lecture 5 Electric flux through area A: Gauss’s law: the total electric flux through a closed surface is equal to the total electric charge inside the surface, divided by ε0. Electric Potential Potential Difference Voltage Gauss’s law, electric field, and surface charge density: Φ E = E⊥ A = EA⊥ Φ E = EA cos θ Φ E = EA = Qencl ε0 ΦE = ∑E ⊥ A= closed surface = σA ε0 E= The work done by the electric field on the electric charge: σ ε0 Qencl ε0 σ= Q A Wa→b = Fe d = qEd The change in electric potential energy equals the PEb − PEa = −Wa→b = −qEd negative of the work done by the electric field: Physics 112, Spring 2010, Jan 22, Lecture 5 Electric Potential Uniform electric field. Electric Potential Energy and Potential Work done by the electric field is similar to that done by gravity (by conservative force!). + near positive plate + near negative plate low potential energy low potential - near positive plate low potential energy high potential - near negative high potential energy plate low potential ΔPE = PEb − PEa = −Wa →b = −qEd The work is done by the electric field to move the charge and it changes the potential energy of the charge. The electric potential or simply the potential: 2 Physics 112, Spring 2010, Jan 22, Lecture 5 Va = PEa q Vb = PEb q - PEa and PEb are the potential energies of some electric charge in the electric filed. Low PE for negative charge Unit for electric potential: volt (1V = 1J/C). high potential energy high potential - Only the difference in potentials of potential difference is measurable! A positive charge has high potential energy when potential V is high. Hence, if we want to speak about Va, we need to know where is zero potential. Zero potential can be chosen at the ground (the Earth) or at infinite distance. Physics 112, Spring 2010, Jan 22, Lecture 5 A negative charge has high potential energy when potential V is low. 3 Physics 112, Spring 2010, Jan 22, Lecture 5 4 1 Electric Potential Difference = Voltage Electric Field and Electric Potential Difference PEb − PEa W = − ba q q Again: The work done by the electric field to move positive charge from a to b: The difference in potential or the potential difference: Vba = Vb − Va = W = Fe d = qEd Unit for potential difference: volt (1V = 1J/C). Another version for work: W = −q(Vb − Va ) = −qVba electric potential difference = voltage If the charge q moves through a potential difference Vab, its potential energy changes by an amount qVba. PEa Va = PEa = qVa PEb − PEa = q(Vb − Va ) = qVba q The electric force accelerates the charge toward the negative plate. PE of the charge decreases while KE increases. PE + KE E=− The minus sign shows that 20 cm = constant 5 6 An electron in TV tube accelerates from rest through a potential difference Vab= 5000 V. 1. What is the change in electric potential energy of the electron? ΔPE = qVba = (−1.6 ×10−19 C )(+5000V ) = −8 ×10−16 J V⎞ ⎛ V = Ed = ⎜ 200 ⎟(0.2 m) = 40 V m⎠ ⎝ The minus sign shows that PE of the charge decreases. ⎛ N ⎞ ⎛V ⎞ Note : the unit of the electric field can be : ⎜ ⎟ or ⎜ ⎟ ⎝C ⎠ ⎝m⎠ 2. What is the speed of the electron as a result of this acceleration? m = 9.1x10-31kg or 20,000 N / C Physics 112, Spring 2010, Jan 22, Lecture 5 V. Physics 112, Spring 2010, Jan 22, Lecture 5 Voltage: V V 120 V = = 20,000 d 0.6 ×10 − 2 m m points in the direction of decreasing potential Acceleration of Electron 2. There is voltage of 120 V between two plates. What is the electric field if the distance between these two plates is 0.6 cm? E= V d The electric field also can be measure in N/C or V/m. 1. There is the electric field of 200 N/C between two metallic plates. What is the voltage between these plates if the distance is 20 cm? - E= Unit for electric field: Electric Field and Voltage + r E Vba d 1 N / C = 1N ⋅ m / C ⋅ m = 1J / C ⋅ m = 1 V / m Physics 112, Spring 2010, Jan 20, Lecture 4 E Vba = − Ed − qVba = qEd The potential of the electric field shows its ability do work on electric charge placed in this electric field. v= − 7 ΔKE = −ΔPE ΔKE + ΔPE = 0 1 2 mv = −q(Vb − Va ) = −qVba 2 2qVba (2)(−1.6 ×10−19 C )(5000 V ) = − = 4.2 ×107 m / s m 9.1×10−31 kg Physics 112, Spring 2010, Jan 22, Lecture 5 8 2 Equipotential Lines Electric Potential and Equipotential Lines Equipotential lines or, in three dimensions, equipotential surfaces, represent constant electric potential. - - - - + + The electric potential difference: d Equipotential lines (the green dashed lines) for electric dipole are perpendicular to the electric field. q − Wb (#1) a PEa =− q q Wa→ # 2 = Wa→ #1 + + + Vba (# 2) = Vba (#1) Potential difference (voltage) between equipotential lines is constant. Low and High Voltage Examples 1.5 V PEb (#1) The work done by the electric force (conservative) is independent of the path taken. 9 Physics 112, Spring 2010, Jan 22, Lecture 5 Vb (#1) a = Vb (#1) − Va = E + a + + PEb (#1) − PEa = −Wa →b (#1) = −qEd b(#2) b(#1) Equipotential lines (the green dashed lines) between two charged parallel plates are perpendicular to the electric field. - Physics 112, Spring 2010, Jan 22, Lecture 5 10 Spark in Air: Electric Breakdown The dielectric breakdown strength of dry air is ~33,000 V/cm = 3,300 000 V/m at Standard Temperature and Pressure (STP): - temperature: 00C, 273 K, or 320F; - pressure 100 kPa, 14.5 psi, or 1 atm. 200,000 V This is only as a rough value since the actual breakdown voltage is highly dependent upon the electrode shape and size. ~ 5,000,000 V 12 V Spark to car door in winter can involve voltage as high as 20,000 V. A high voltage is not necessarily dangerous if it cannot deliver substantial current. Physics 112, Spring 2010, Jan 22, Lecture 5 11 Physics 112, Spring 2010, Jan 22, Lecture 5 12 3 Electric Field Between Clouds and Earth (#1) Charged clouds + + - - - + + + + - - - - Charged clouds + - Electric Field Between Clouds and Earth (#2) - - If electric field is uniform, breakdown is equally likely to happed anywhere. Electric breakdown is more likely to happed here. Is it true? 108 d Why you should not seek shelter under a tree during a storm? + V E= All this is one conductor E V = Ed + + d The electric field is stronger between the clouds and conducting rod: smaller distance! + + + Wet tree V (V/m) d Conducting (metal) rod + Ground Ground Physics 112, Spring 2010, Jan 22, Lecture 5 13 Physics 112, Spring 2010, Jan 22, Lecture 5 14 Potential Difference at Power Line How can a bird stand on a high voltage power line and not get zapped? The potential difference between its feet is so small that very little current flows through the bird’s body. Can somebody survive if touching the wire under 100,000 V as shown in the picture? 1) no 2) yes Physics 112, Spring 2010, Jan 22, Lecture 5 15 4