Lecture 4 Electric Potential and/ Potential Energy Ch. 25PowerPoint PresentationSlide 3Slide 4Potential Energy and Electric potentialSlide 6Slide 7Slide 8Example for a battery in a circuitExample of a proton accelerated in a uniform fieldWhat is the electric potential when moving from one point to another in a field due to a point charge?Potential of a point charge at a distance RElectric potential for a positive point chargeSlide 14What is the electric potential due to several point charges?Slide 16Potential due to a dipoleSlide 18Potential due to a ring of chargePotential due to a line chargeA new method to find E if the potential is known. If we know V, how do we find E?Equipotential SurfacesSlide 23Slide 24Slide 25Dielectric Breakdown: Application of Gauss’s LawThis explains why:How does a conductor shield the interior from an exterior electric field?A metal slab is put in a uniform electric field of 106 N/C with the field perpendicular to both surfaces.What is the electric potential of a uniformly charged circular disk?1Lecture 4 Electric Potential and/ Potential Energy Ch. 25•Review from Lecture 3•Cartoon - There is an electric energy associated with the position of a charge.•Opening Demo - •Warm-up problems •Physlet •Topics•Electric potential energy and electric potential•Calculation of potential from field•Potential from a point charge•Potential due to a group of point charges, electric dipole•Potential due to continuous charged distributions•Calculating the filed from the potential•Electric potential energy from a system of point charge•Equipotential Surface•Potential of a charged isolated conductor•Demos•teflon and silk•Charge Tester, non-spherical conductor, compare charge density at Radii•Van de Graaff generator with pointed objects23QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.4QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.5Potential Energy and Electric potential•The electric force is mathematically the same as gravity so it too must be a conservative force. We will find it useful to define a potential energy as is the case for gravity. Recall that the change in the potential energy in moving from one point a to point b is the negative of the work done by the electric force.• = - W = -Work done by the electric force =•Since ,  U = and•Electric Potential difference = Potential energy change/ unit charge • (independent of path, ds)−q0E ⋅dsab∫∫⋅−badsFabUUU −=ΔF =q0EΔV =ΔUq0∫⋅−=−=Δ dsEVVVabSI unit of electric potential is volt (V):1 Volt = 1 Joule/Coulomb (1 V = 1 J/C)• Joule is too large a unit of energy when working at the atomic or molecular level, so use the electron-volt (eV), the energy obtained when an electron moves through a potential difference of 1 V. 1 eV = 1.6 x 10-19 J6 (independent of path, ds)Therefore, electric force is a conservative force. = - Work done by the electric force =€ − F ⋅ dsif∫ΔU = Uf− UiqUVΔ=Δ∫⋅−=−=Δ dsEVVVifyx7•The potential difference is the negative of the work done per unit charge by an electric field on a positive unit charge when it moves from one point to another.• V is a scalar not a vector. Simplifies solving problems.•We are free to choose V to be 0 at any location. Normally V is chosen to be 0 at the negative terminal of a battery or 0 at infinity for a point charge. ΔV =−Wq0= −rFq0⋅drs∫= −rE ⋅drs∫8Example of finding the potential difference in a Uniform FieldWhat is the electric potential difference for a unit positive charge moving in an uniform electric field from a to b?EEdabx direction)(abbabaxxEdxEdsEV −−=−=⋅−=Δ∫∫dEdV −=ΔVqU Δ=ΔqEdU −=ΔdV =−EdxE =−dV /dx9Example for a battery in a circuit•In a 9 volt battery, typically used in IC circuits, the positive terminal has a potential 9 v higher than the negative terminal. If one micro-Coulomb of positive charge flows through an external circuit from the positive to negative terminal, how much has its potential energy been changed?qVVVqUVab)90( −=−=Δ=ΔPotential energy is lower by qU 9−=Δ9 μJCV6101)9( −××−=JoulesU6109−×−=ΔΔU = − 9 microJoules = − 9 μJWe also assumed that the potential at b was 010Example of a proton accelerated in a uniform fieldA proton is placed in an electric field of E=105 V/m and released. After going 10 cm, what is its speed?Use conservation of energy.a b+E = 105 V/md = 10 cmmqEdv2=v =2×1.6×10−19C ×105Vm×0.1m1.67×10−27kgv =1.4×108msEdVVVab−=−=ΔΔK = qEdUK Δ−=ΔΔU = qΔV = −qEd0=Δ+Δ KU12mv2=qEd11What is the electric potential when moving from one point to another in a field due to a point charge? ΔV = −rE ⋅drr∫ rE =kqr2ˆr Vf−Vi=−rE ⋅drrif∫12 Vf−Vi=−rE ⋅dˆrR∞∫=−kqcos0o1r2dR∞∫r =kq1rR∞=kq(1∞−1R)RkqV =041πε=keqn 25-26Replace R with rV =14πε0qrVf−Vi=0−Vi=−kqRPotential of a point charge at a distance R Vf−Vi=−rE ⋅dˆrif∫13Electric potential for a positive point chargeV(r) =kqrr = x2+y2•V is a scalar•V is positive for positive charges, negative for negative charges.•r is always positive.•For many point charges, the potential at a point in space is the simple algebraic sum (Not a vector sum)14Hydrogen atom. • What is the electric potential at a distance of 0.529 A from the proton? 1A= 10-10 mElectric potential due to a positive point charger = 0.529 AmCCNmRkqV101922910529.106.11099.8−−×××⎟⎠⎞⎜⎝⎛×==V =27.2JC=27.2VoltsWhat is the electric potential energy of the electron at that point?U = qV= (-1.6 x 10-19 C) (27.2 V)= - 43.52 x 10-19 Jor - 27.2 eV where eV stands for electron volts.Total energy of the electron in the ground state of hydrogen is - 13.6 eVAlso U= 2E = -27.2 eV. This agrees with above formula.15What is the electric potential due to several point charges?•For many point charges, the potential at a point in space is the simple algebraic sum (Not a vector sum)⎟⎠⎞⎜⎝⎛++=332211rqrqrqkVV =kqirii∑r1 xr3yr2q1q2q316QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.17Potential due to a dipoleFor two point charges, the total potential is the sum of the potentials of each point charge.batotaldipoleVVVV ,So +==⎟⎠⎞⎜⎝⎛ −+=+=babadipoler)q(rqkVVV⎟⎠⎞⎜⎝⎛−=baabrrrrkqWe are interested in the