Chapter 16 Electric Energy and Capacitance 16.1 Potential difference and electric potential
He is full of potential at this moment
• Potential to do a lot of damage Potential energy
Recall Work from PHY101 • Potential energy is always related to a force • In the presence of a force (gravity or electrical force), potential energy increases when an object is moved in the opposite direction of the force A
++++++++++++ A
• Has to do with gravity (a force)
+++++++++++++
+
A
-
• Has to do with height, or distance in the direction of the force
B
-
B+ -----------------
B ------------------
EPEA
EPEA
EPEB
EPEB
Quantitatively speaking A
B
PE = PEfinal-PEinitial = EB-EA = F (xB-xA) = -(mg)(xA) = -mgh PE = - (F)(disp.) F parallel to disp. (xA-xB)
++++++++++++ A
+
B+ -----------------
EPE = EPEB-EPEA = -(F x) = -(Eq x)
+++++++++++++ A
Work and Potential Energy
-
B ------------------
EPE = EPEB-EPEA = -(F x) = -(-Eq x)
F parallel to x F antiparallel to x
• There is a uniform field between the two plates • As the charge moves from A to B, work is done on it • W = Fd=q Ex (xf – xi) • ΔPE = - W = - q Ex x – Only for a uniform field
PEB-PEA = negative A positive charge loses electrical potential energy when it is moved in the direction of the electric field
Energy and Charge Movements • A positive charge loses electrical potential energy when it is moved in the direction of the electric field • A negative charge loses electrical potential energy when it moves in the direction opposite the electric field • If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy – As it gains kinetic energy, it loses an equal amount of electrical potential energy
++++++++++++ A
+ x
B+ -----------------
EPE = -(Eq x)
• EPE = Vq • For a positive charge, the higher the potential, the higher the potential energy • For a negative charge, the higher the potential, the more negative (or lower) the potential energy
Potential Difference (NOT PE!!) • The potential difference between points A and B is defined as the change in the potential energy (final value minus initial value) of a charge q moved from A to B divided by the size of the charge – ΔV = VB – VA = ΔEPE / q
• Potential difference is not the same as potential energy
Energy is energy (regardless what the source is, chemical, electric, nuclear…) Energy conservation:
The Electron Volt • The electron volt (eV) is defined as the energy that an electron gains when accelerated through a potential difference of 1 V – Electrons in normal atoms have energies of 10’s of eV – Excited electrons have energies of 1000’s of eV – High energy gamma rays have energies of millions of eV
• 1 eV = 1.6 x 10-19 J
A unit for energy: 1 eV = energy needed to move an electron over 1 V = 1.6 x 10-19 C x 1 V = 1.6 x 10-19 J
16.2 The Electric Potential Difference Created by a Point Charge
Electric Potential Energy of Two Charges • If the charges have the same sign, PE is positive – Positive work must be done to force the two charges near one another – The like charges would repel
• If the charges have opposite signs, PE is negative – The force would be attractive – Work must be done to hold back the unlike charges from accelerating as they are brought close together
Force, field, EPE, V Problem Solving with Electric Potential • Draw a diagram of all charges – Note the point of interest
• Calculate the distance from each charge to the point of interest • Use the basic equation V = keq/r – Include the sign – The potential is positive if the charge is positive and negative if the charge is negative
• Field (vector) & potential (scalar); environment associated with a charge or charges – Describe the surrounding of a charge (starts with ONE charge) – For one charge: E = kq/r2, V = kq/r • Force (vector) & EPE (scalar): interaction between two charges – Describe the interaction between two charges (at least ONE PAIR of charges) – For one pair of charges: F = kq1q2/r2, EPE = kq1q2/r – Our own potential energy is from the interaction between us and the Earth • Pay attention to the directions and magnitudes for vectors, but signs for scalars • Considering things are all invisible to our eyes, we have to think through the process – you are not alone
16.3 Potentials and charged conductors Application – Electrostatic Precipitator
• The whole surface of a conductor has the same potential • Potential remains the same when extension cords (conductors) are used.
• It is used to remove particulate matter from combustion gases • Reduces air pollution • Can eliminate approximately 90% by mass of the ash and dust from smoke • Recovers metal oxides from the stack
Capacitance • A capacitor is a device used in a variety of electric circuits • The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates)
16.6&7 Capacitance & parallel plate capacitor
q = CV C: capacitance
• Computers use capacitors in many ways
Unit: Farad (F)
– Some keyboards use capacitors at the bases of the keys – When the key is pressed, the capacitor spacing decreases and the capacitance increases – The key is recognized by the change in capacitance
Dielectrics are not covered
Capacitors in Circuits • A circuit is a collection of objects usually containing a source of electrical energy (such as a battery) connected to elements that convert electrical energy to other forms • A circuit diagram can be used to show the path of the real circuit
• Things in series V1 + V2 = Vbattery
• Things in parallel
Some electrical thing, light bulb, capacitors, TVs, …
V1 = V2 = Vbattery
Capacitors in Series
Capacitors in Parallel
• When in series, the capacitors are connected end-to-end • The magnitude of the charge must be the same on all the plates
• The total charge is equal to the sum of the charges on the capacitors – Qtotal = Q1 + Q2
• The potential difference across the capacitors is the same – And each is equal to the voltage of the battery
Application
Energy Stored in a Capacitor • Energy stored = ½ Q ΔV • From the definition of capacitance, this can be rewritten in different forms
Energy
1 Q V 2
1 C V2 2
Q2 2C
• Defibrillators – When fibrillation occurs, the heart produces a rapid, irregular pattern of beats – A fast discharge of electrical energy through the heart can return the organ to its normal beat pattern
• In general, capacitors act as energy reservoirs that can be slowly charged and then discharged quickly to provide large amounts of energy in a short pulse