Electric potential energy

Chapter 17Electric Potential

Physics Kahuna’s Review of some vital information:1. Work takes place when a force acts over a distance. [W = Fr]2. The unit for work is the Joule (J); A Joule is a newtonmeter.3. Potential energy from gravity is U g = mgh4. The force of gravity acting on an object with mass isalways directed towards the center of the earth.5. When you lift an object you do work on it. As its heightis increased, its potential energy increases. The workYOU do on it is equal to the increase in potentialenergy of the thing.Looking at electric fields around a changed object we find that we also havework being done and potential energy changes being made when we movecharges around that object.

Electric PotentialEnergy•Electric potential energy: Energy storedin an electrical field due to the position ofa charge in the electrical field.•We know that potential energy is force xdistance: U = Fr.•The force acting between the electronand the proton is: 1 q qF4 o1 22•We can plug in Coulomb’s law for theforce in the potential energy equation andget1 q1q2U 4 orr

Electrical Potential Energy• EXAMPLE : An electron in a hydrogen atom isat it’s lowest energy state. It is at a distanceof 5.29 x 10 -11 m from the proton in thenucleus. What is the potential energy relativeto the proton? [4.35 x 10 -18 J]

17.1 Electrostatic Potential Energy andPotential DifferenceWORK IN THE ELECTRIC FIELD:Work is done when a particle is moved from one point toanother in an electric field.•If the two charges are unlike•Pull the charges apart– PE increases (likegravity)•Push the charges together – PE decreases•If the two charges are alike•Pull charges apart – PE decreases•Push charged together – PE increasesChange in electric potential energy is negativeof work done by electric force:

Electrical Potential Energy• Electrical PE = charge x electrical field strength x displacement[This equation is only valid for a uniform electrical field]• Remember, it is not the potential that has any meaning, it isthe difference in potential energy. Electrical potential energyis like gravitational potential energy.• The unit for electric potential energy is the Joule.• Example 1: As a particle moves 10.0 m along an electricfield of strength 75 N/C, its electrical potential energy isdecreased by 4.8 x 10 -16 J. What is the particle’s charge?• 6.4 x 10 -19 C

The electrical force energy and electrical potential energy for a pair of pointparticles are proportional to the produce of the charges of the particles.FEkqq2kqq1 1 2U ( 0 at r )2EUErrWhy is no negative sign written for the potential energy equation?If the two charges have opposite signs, the force is an attractive one. Thepotential energy should be negative, as it is for the attractive force ofgravity. With opposite signs, the product q 1 q 2 is negative and the potentialenergy has the correct sign. If the two charges instead have the samesign, the product q 1 q 2 is positive. The electric force is repulsive, thepotential energy increases as they move closer together. So it gives us thecorrect sign.

We know that work is: W = FrThe force exerted on a test charge in an electric field is:E = F/q or F = qEPut these two together:W = Fd = (qE)d = qEdThis gives us an equation fo the work done in anelectric field in moving a charge from one position toanother.The work done in moving the charge is equal to thechange in potential energy. Therefore we can write:U = -WThe negative sign simply means that the potentialenergy will increase if the charge is negative ordecrease if the charge is positive.U = -qEd

Similarities between gravitational and electrical potentialenergy:•In both cases, the potential energy depends on only thepositions of various objects, not on the path they took to getto these positions. [Both are conservative forces].•Only changes in potential energy are physically significant,so we are free to assign the potential energy to be zero atany one convenient point.•For two point particles, we usually choose U = 0 when theparticles are infinitely far apart.•Both the gravitational and electrical forces exerted by onepoint particle on another are inversely proportional to thesquare of the distance between them.

Electric Potential• Just as the electric field is defined as theelectric for e per unit charge, the electricpotential V, is defined as the electric potentialenergy per unit charge.• Electric potential:UV q• The SI Unit for electric potential is theJoule/ coulomb, which is named the volt.• Be careful to distinguish the electric potentialfrom electric potential energy.E

•Potential Difference: Instead of looking at the total potentialenergy, we can look at the potential energy per Coulomb ofcharge.•This, the potential energy per charge is called the potentialdifference.•Potential Difference Change in potential energy per Charge•The symbol for potential difference is V or V.•V Potential difference = U/q•U = -qEd andUqEdEdqqV = Ed

Potential Difference1 V = 1 J/C• Electric potential is a scalar quantity. Potentials do not havedirection in space.• When a point charge q moves from point A to point B, it movesthrough a potential difference. The potential difference is thecharge in electric potential energy per unit charge.U qV• The electrical force on a charge is always directed toward regionsof lower electric potential energy, just as the gravitational force onan 0bject is directed toward regions of lower gravitationalpotential energy.• For a positive charge lower potential means lower potential, for anegative charge, lower potential energy means higher potential.

Electrostatic Potential Energy andPotential DifferenceElectrical potential difference: The measure of the difference in theelectrical potential energy between two positions in space divided by thecharge.The unit for potential difference is the Volt.1 V = 1 J/CPotential difference is a measure of the difference in energy per unitchargeVUqEUnit of electric potential: the volt (V).1 V = I J/C.

17.1 Electrostatic Potential Energy andPotential DifferenceAnalogy between gravitational and electricalpotential energy:

Relation between Electric Potential andElectric FieldSince work equals in the change in PE, thenWork is charge multiplied by potential:Work is also force multiplied by distance:

Potential Difference• Potential difference in a Uniform electric fieldΔV = Ed• Keep in mind that the displacement must be parallel tothe electrical field. Motion perpendicular to the fielddoes not change the electrical potential energy.• Example: A proton is released from rest in a uniformelectric field with a magnitude of 8.0 x 10 4 V/m. theproton is displaced 0.50 m as a result. (a) Find thepotential difference between the proton’s initial andfinal positions. (b) Find the change in electricalpotential energy of the proton as a result.• [(a.) -4. x 10 4 V (b) -6.4 x 10 -15 J

Examples1. The potential difference between two points is21.0V. What amount of work is needed tomove a 2.00 μC charge within the field?[2.40 x 10 -5 J]2. Two charged plates are 5.00 cm apart. Theelectric field between them is 775 N/C. What is(a) the potential difference between the platesand (b) what work is done moving an electronfrom one plate to another?

Example• A proton is released from rest in a uniformelectric field , E = 8.0 x 10 4 V/m. It is directedalong the x axis. It’s displacement is 0.50 m inthe direction of the field. (a) What is thechange in potential difference? (b) What is thechange in electrical potential energy? (c) Whatis the velocity after it traveled 0.50 m?