1Review from yesterdayPlease answer PROBLEM 3 in Knight on page 716 while we are waiting to start.“It takes 3.0 μJ to move a 15nC charge from A to B…”2Review from yesterdayPlease answer PROBLEM 17 in Knight on page 717 while we are waiting to start.“What is the potential of an ordinary AA or AAA battery?...”3Electric Potential• Electric potential energy• Electric potential• Electric potential and electric field• Capacitors • Dielectrics• Electric energy stored in capacitors4Potential Energy• Energy stored in a system• Different types of potential energy• Gravitational • Elastic • Electrical5Electric Potential Energy• Moving an electric charge in an electric field requires or releases energy, U (Joules).• (Note we use U for energy because the electric field is E)• The energy, U, is proportional to charge – just as the force is proportional to charge.6Electric Potential• We define an Electric Potential, V, as the energy per unit charge, q:• V = U/q• Describes what would happen to a charge if it was placed in the electric field• This electrical potential is a property of the system of the surrounding charges• It has units of Joules/Coulomb, or Volts7Electric Potential• Electric potential is a concept we use to be able to predict and calculate energies to move charges• The energy needed to move a charge from one potential V1to another, V2, is simply• ΔU = q(V2– V1)• It is the same physical quantity on batteries8Electric Potential•The electric potential is a property of the source charges, we exclude the charge we are moving.•A contour map of points of equal potentials will give us lines where the potential energy of a charge is constant•Electric potential has magnitude but no direction – it is a scalar9electronVolts• U=qV, units are usually Joules• Sometimes (especially in Atomic Physics) it is useful to express the energy in units of electrons*Volts• 1 eV = Charge on electron * 1 Volt• 1eV = 1.6x10-19Joules• The energy required to move an electron or proton through a potential of 1V10Electric Potential in a Parallel Plate Capacitor• Recall Energy or Work = Force x Distance• From yesterday, F=qE• From today, Work = Electric Potential, U• To move a distance x in constant field between plates : U=q|E|x• The electric potential will bexAεQ=x=qU=V0E11Potential inside a Parallel Plate Capacitor•Electric potential is proportional to the distance, x, from the bottom plate•Total Voltage across capacitorxAQxV0)(dAQVCapacitor0ActivPhysics12Field inside a Parallel Plate Capacitor•Electric field inside the plates is constant.• inversely proportional to the plate separationdVEAQ0E13Potential of a Point Charge• The potential, V, is defined by V=U/q (Energy per unit charge)• Energy is Force times distance• For parallel plates, the field and force are constant, but near a point charge, force is inversely proportional to r2. AεqQ=q=0EF 2rqQ=q= EFF14Potential of a Point Charge• It can be shown that when a force is inversely proportional to r2, the potential energy will be inversely proportional to r.• Remember, U is the potential energy required to place q next to QrqQK=UAεqQd=U015Potential of a Point Charge• Now we apply the definition of potential: V=U/q. Energy per unit charge• The potential of a point charge is thereforerQKV AQdV0rπεQ=rQK=V0416Electric Potential of a Charged Sphere• For a point source we have• Replacing with a metal sphere, the field outside the sphere stays the same.• And we can calculate the charge on a sphere from its potentialrQKV sphereRQK=VKRV=Qsphere17Electric Potential is a scalar• Potential has magnitude but no direction• The potential at a point is the sum of the potentials from all charges in the systemiiirqK=V18Electric Potential in a ConductorWe know that• Excess charge in a conductor moves to the surface• Electric field inside is Zero• Exterior field is perpendicular to the surface• Field strength is largest at sharp cornersWe can add• The entire conductor is at the same potential• The surface is an equipotential surface19Capacitance• Experimentally, the voltage across a capacitor, V, is proportional to the amount of charge on the plates, Q: • Q=CV• C is the capacitance and has units Coulombs/Volt or Farads20Parallel Plate Capacitor in a vacuum• From the definition of Capacitance• And the equations for the electric field• We can find the capacitance of parallel platesdACAQdVECVQ0021Dielectrics• Dielectrics can be used to increase the effects of a capacitor• The dipoles align (polarize) to reduce the electric field inside the material• The electric fields of the dipoles counteract the field from the plates22Dielectrics• This property κ is expressed as the dielectric constant and is a property of the material• Vacuum and Air = 1, de-ionized water=80materialvacuumEE=κ23Dielectrics• This will increase the capacitance – by factors of 100 for the best dielectric materialsdAκε=C024Energy stored in capacitors• When we charge a capacitor to a voltage V, work is being done against a voltage difference• Starting Voltage = 0• Ending Voltage = V• Average Voltage Vave= V/2• Energy is U=QVave=CV2/225Energy stored in the fieldThe energy in the capacitor can be expressed as an energy density, u J/m3, inside the capacitor22121(Ad)Eκε=CV=U02221Eκε=AdU=u026Summary• Electric potential energy• Electric potential• Electric potential and electric field• Capacitors • Dielectrics• Electric energy stored in capacitors27HomeworkKnight Problems51, 52, 61, 65, 68, 71, 74,
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