Electric Potential Electric Potential & Electric & Electric

Potential EnergyPotential Energy

Electric Potential Electric Potential EnergyEnergy

The electrostatic force is a The electrostatic force is a conservative (conservative (=“path independent”=“path independent”) ) forceforce

It is possible to define an electrical It is possible to define an electrical potential energy function with this potential energy function with this forceforce

Work done by a conservative force is Work done by a conservative force is equal to the negative of the change in equal to the negative of the change in potential energypotential energy

Work and Potential EnergyWork and Potential Energy

There is a uniform There is a uniform field between the field between the two platestwo plates

As the positive As the positive charge moves from A charge moves from A to B, work is doneto B, work is done

WWABAB==F dF d==q E dq E d

ΔΔPEPE =- =-WW ABAB=-=-q E dq E d only for a uniform only for a uniform

fieldfield

Potential Difference Potential Difference (=“Voltage Drop”)(=“Voltage Drop”)

The potential difference between The potential difference between points A and B is defined as the points A and B is defined as the change in the potential energy change in the potential energy (final value minus initial value) of a (final value minus initial value) of a charge charge qq moved from A to B divided moved from A to B divided by the size of the chargeby the size of the charge ΔΔVV = = VVBB – – VVAA = Δ = ΔPEPE / /qq

Potential difference is Potential difference is not not the same the same as potential energyas potential energy

Potential Difference, cont.Potential Difference, cont. Another way to relate the energy and the Another way to relate the energy and the

potential difference: potential difference: ΔΔPEPE = = qq Δ ΔVV Both electric potential energy and potential Both electric potential energy and potential

difference are difference are scalarscalar quantities quantities Units of potential differenceUnits of potential difference

V = J/CV = J/C A special case occurs when there is a A special case occurs when there is a

uniform electric fielduniform electric field VVBB – – VVAA= -= -EdEd

Gives more information about units: Gives more information about units: N/C N/C = V/m= V/m

Energy and Charge Energy and Charge MovementsMovements

A A positivepositive charge charge gainsgains electrical electrical potential energy when it is moved in a potential energy when it is moved in a direction opposite the electric fielddirection opposite the electric field

If a charge is released in the electric field, If a charge is released in the electric field, it experiences a force and accelerates, it experiences a force and accelerates, gaining kinetic energygaining kinetic energy As it gains kinetic energy, it loses an equal As it gains kinetic energy, it loses an equal

amount of electrical potential energyamount of electrical potential energy A A negativenegative charge charge losesloses electrical electrical

potential energy when it moves in the potential energy when it moves in the direction opposite the electric fielddirection opposite the electric field

Energy and Charge Energy and Charge Movements, contMovements, cont

When the electric field is When the electric field is directed downward, point directed downward, point B is at a lower potential B is at a lower potential than point Athan point A

A positive test charge A positive test charge that moves from A to B that moves from A to B loses electric potential loses electric potential energyenergy

It will gain the same It will gain the same amount of kinetic energy amount of kinetic energy as it loses potential as it loses potential energyenergy

Summary of Positive Summary of Positive Charge Movements and Charge Movements and EnergyEnergy

When a positive charge is placed in When a positive charge is placed in an electric fieldan electric field It moves in the direction of the fieldIt moves in the direction of the field It moves from a point of higher It moves from a point of higher

potential to a point of lower potentialpotential to a point of lower potential Its electrical potential energy Its electrical potential energy

decreasesdecreases Its kinetic energy increasesIts kinetic energy increases

Summary of Negative Summary of Negative Charge Movements and Charge Movements and EnergyEnergy

When a negative charge is placed in When a negative charge is placed in an electric fieldan electric field It moves opposite to the direction of It moves opposite to the direction of

the fieldthe field It moves from a point of lower potential It moves from a point of lower potential

to a point of higher potentialto a point of higher potential Its electrical potential energy Its electrical potential energy

decreasesdecreases Its kinetic energy increasesIts kinetic energy increases

Example: A proton moves from rest in an electric field of Example: A proton moves from rest in an electric field of

8.08.0101044 V/m along the +V/m along the +xx axis for 50 cm. Find a) the axis for 50 cm. Find a) the change in in the electric potential, b) the change in the change in in the electric potential, b) the change in the electrical potential energy, and c) the speed after it has electrical potential energy, and c) the speed after it has moved 50 cm. moved 50 cm.

a) a) VV=-=-EdEd=-(8.0=-(8.0101044 V/m)(0.50 m)=-4.0 V/m)(0.50 m)=-4.0101044 V V

b) b) PEPE==qq VV=(1.6=(1.61010-19-19 C)(-4.0 C)(-4.0 101044 V)=-6.4 V)=-6.4 1010-15-15 JJ KEi+PEi=KEf+PEf, KEi=0

KEf=PEi-PEf=-PEPE,,

mmppvv22/2=6.4/2=6.41010-15-15 J J

mmpp=1.67=1.671010-15-15 kg kg

s/m108.2kg1067.1

)J104.6(2 627

15

v

16.2 Electric Potential 16.2 Electric Potential of a Point Chargeof a Point Charge

The point of zero electric potential The point of zero electric potential is taken to be at an infinite is taken to be at an infinite distance from the chargedistance from the charge

The potential created by a point The potential created by a point charge charge qq at any distance at any distance rr from the from the charge ischarge is

r

qkV e if r, V=0 and if r=0, V

V decreases as 1/r, and, as a consequence, E decreases 1/r2.

Electric Potential of an Electric Potential of an electric Dipoleelectric Dipole

-q

+q

Electric Potential of Electric Potential of Multiple Point ChargesMultiple Point Charges

Superposition principle appliesSuperposition principle applies The total electric potential at some The total electric potential at some

point P due to several point point P due to several point charges is the charges is the algebraicalgebraic sum of the sum of the electric potentials due to the electric potentials due to the individual chargesindividual charges The algebraic sum is used because The algebraic sum is used because

potentials are scalar quantitiespotentials are scalar quantities

Electrical Potential Energy Electrical Potential Energy of Two Chargesof Two Charges

VV11 is the electric is the electric potential due to potential due to qq11 at at some point some point PP11

The work required to The work required to bring bring qq22 from infinity to from infinity to PP11 without acceleration without acceleration is is qq22EE11dd==qq22VV11

This work is equal to This work is equal to the potential energy of the potential energy of the two particle systemthe two particle system

r

qqkVqPE 21

e12

Notes About Electric Notes About Electric Potential Energy of Two Potential Energy of Two ChargesCharges

If the charges have the If the charges have the samesame sign, sign, PEPE is is positivepositive Positive work must be done to force the two Positive work must be done to force the two

charges near one anothercharges near one another The like charges would repelThe like charges would repel

If the charges have If the charges have oppositeopposite signs, signs, PEPE is is negativenegative The force would be attractiveThe force would be attractive Work must be done to hold backWork must be done to hold back the unlike the unlike

charges from accelerating as they are charges from accelerating as they are brought close togetherbrought close together

Example: Finding the Electric Example: Finding the Electric Potential at Point P (apply Potential at Point P (apply VV==kkeeqq//rr).).

5.0 C -2.0 C

V1060.3)m0.4()m0.3(

)C100.2()C/Nm1099.8(

,V1012.1m0.4

C100.5)C/Nm1099.8(

3

22

6229

2

46

2291

V

V

Superposition: Vp=V1+V2

Vp=1.12104 V+(-3.60103 V)=7.6103 V

Problem Solving with Problem Solving with Electric Potential (Point Electric Potential (Point Charges)Charges)

Remember that potential is a scalar Remember that potential is a scalar quantityquantity So no components to worry aboutSo no components to worry about

Use the superposition principle when you Use the superposition principle when you have multiple chargeshave multiple charges Take the algebraic sumTake the algebraic sum

Keep track of signKeep track of sign The potential is positive if the charge is The potential is positive if the charge is

positive and negative if the charge is negativepositive and negative if the charge is negative Use the basic equation Use the basic equation VV = = kkeeqq//rr

Potentials and Charged Potentials and Charged ConductorsConductors

WW =- =-PEPE= -= -qq((VVBB – – VVAA)) , no work is , no work is required to move a charge between two required to move a charge between two points that are at the same electric points that are at the same electric potential potential WW=0 when =0 when VVAA==VVBB

All points on the surface of a charged All points on the surface of a charged conductor in electrostatic equilibrium conductor in electrostatic equilibrium are at the same potentialare at the same potential

Therefore, the electric potential is a Therefore, the electric potential is a constant everywhere on the surface of constant everywhere on the surface of a charged conductor in equilibriuma charged conductor in equilibrium

Overview: Conductors in Overview: Conductors in EquilibriumEquilibrium

The conductor has an The conductor has an excess of positive chargeexcess of positive charge

All of the charge resides at All of the charge resides at the surfacethe surface

EE = 0 inside the conductor = 0 inside the conductor The electric field just The electric field just

outside the conductor is outside the conductor is perpendicular to the surfaceperpendicular to the surface

The potential is a constant The potential is a constant everywhere on the surface everywhere on the surface of the conductor of the conductor

The potential everywhere The potential everywhere inside the conductor is inside the conductor is constant and equal to its constant and equal to its value at the surfacevalue at the surface

The Electron VoltThe Electron Volt

The electron volt (eV) is defined as the The electron volt (eV) is defined as the energy that an electron (or proton) energy that an electron (or proton) gains when accelerated through a gains when accelerated through a potential difference of 1 Vpotential difference of 1 V Electrons in normal atoms have energies of Electrons in normal atoms have energies of

10’s of eV10’s of eV Excited electrons have energies of 1000’s of Excited electrons have energies of 1000’s of

eVeV High energy gamma rays have energies of High energy gamma rays have energies of

millions of eVmillions of eV 1 V=1 J/C 1 V=1 J/C 1 eV = 1.6 x 10 1 eV = 1.6 x 10-19-19 J J

Equipotential SurfacesEquipotential Surfaces

An An equipotential surfaceequipotential surface is a is a surface on which all points are at surface on which all points are at the same potentialthe same potential No work is required to move a charge No work is required to move a charge

at a constant speed on an at a constant speed on an equipotential surfaceequipotential surface

The electric field at every point on an The electric field at every point on an equipotential surface is perpendicular equipotential surface is perpendicular to the surfaceto the surface

Equipotentials and Electric Equipotentials and Electric Fields Lines (Positive Fields Lines (Positive Charge):Charge):

The equipotentials The equipotentials for a point charge for a point charge are a family of are a family of spheres centered on spheres centered on the point chargethe point charge

The field lines are The field lines are perpendicular to the perpendicular to the electric potential at electric potential at all pointsall points

Equipotentials and Electric Equipotentials and Electric Fields Lines (Dipole):Fields Lines (Dipole):

Equipotential lines Equipotential lines are shown in blueare shown in blue

Electric field lines Electric field lines are shown in are shown in orange orange

The field lines are The field lines are perpendicular to perpendicular to the equipotential the equipotential lines at all pointslines at all points