PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 10
Chapter 26
Capacitance
Physics II
My Capacitance is limited
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Today we are going to discuss:
Chapter 26:
Section 26.2 The Geometry of Potential and Field Section 26.3 A Conductor in Electrostatic equilibrium Section 26.5 Capacitance and Capacitors
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Connecting Potential and Field (Review)
sdEVVVf
iif
We can find the potential difference between two points if we know the electric field.
dxdVEx
dydVEy
dzdVEz
Atwhichpointistheelectricfieldstronger?
A) AtxAB) AtxBC) Thefieldisthesamestrengthatboth
D)There’snotenoughinformationtotell
|E| = slope of potential graph
dxdVEx
At XA a slope is larger
ConcepTest E from the electric potential
Anelectronisreleasedfromrestatx=2minthepotentialshown.Whatdoestheelectrondorightafterbeingreleased?
A) Stayatx 2m
B)Movetotheright( x)atsteadyspeed
C)Movetotherightwithincreasingspeed
D)Movetotheleft(x)atsteadyspeed
E)Movetotheleftwithincreasingspeed
1) Slope of V negative => Ex is positive (field to the right).2) Electron is negative => force to the left.
3) Force to the left => acceleration to the left.
xEqxF
dxdVEx
maFx
a
ConcepTest My Favorite question
qEFx
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Geometry of Potential and Field
Let s be along an equipotential line, dsdVEs
where V=const. So dV=0. dsdVEs
0
0So, it is impossible to have an electric field along equipotential lines,
linesialequipotentE
equipotential lines
Whichsetofequipotentialsurfacesmatchesthiselectricfield?
A)
B)
C)
D)
E)
F)
E
ConcepTest Geometry E and V
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Potential of a Conductor
i
f
sdEVVVf
iif
0V if VV
Aconductorinelectrostaticequilibriumisatthesamepotential.
constV
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Electric Battery
A battery transforms chemical energy into electrical energy.
Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them.
Atom of Zn gets dissolved leaving two electrons behind
Two electrons get attracted by the ion of Zn leaving behind positively charged electrode
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
CapacitorstoresenergyAcapacitorisasystemthatstorespotentialenergyinaformofanelectricfield.
Ugh!It’s just energy
Capacitor
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Capacitance (definition)
The ratio of the charge Q to the potential difference VC is called the capacitance C:
The SI unit of capacitance is the farad:
≝
VC
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Parallel-plate capacitor
In its simplest form, a capacitor consists of a pair of parallel metal plates separated by air/insulating material.
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Parallel-plate capacitor
Let’sfindcapacitanceofaparallel‐platecapacitor
Capacitanceisapurelygeometricpropertyoftwoelectrodesbecauseitdependsonlyontheirsurfaceareaandspacing.
≝
E
d
Aarea
+Q–Q
Theelectricfieldbetweentheplatesisη ‐ surfacechargedensity
(Eq.25.26)Thepotentialdifferencebetweenplates:
WeneedtofindQandΔV:
≝ =
Thisgivesthecapacitance:
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Parallel-plate capacitor
WecanincreasecapacitancebyincreasingareaAbymaking“arollofmetalandinsulator”
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Parallel-plate capacitor/keyboard
Capacitorsareimportantelementsinelectriccircuits.Theycomeinavarietyofsizesandshapes.
Thekeysonmostcomputerkeyboardsarecapacitorswitches.Pressingthekeypushestwocapacitorplatesclosertogether,increasingtheircapacitance.
Whatisthecapacitanceofthesetwoelectrodes?
A) 8 nF
B) 4 nF
C) 2 nF
D) 1 nF
E) Some other value
ConcepTest Capacitance
≝
Sincethebatterystaysconnected,thepotential
differencemustremainconstant!+Q –Q
Aparallel‐platecapacitorinitiallyhasavoltageof400V andstaysconnectedtothebattery.Iftheplatespacingisnowdoubled, whathappens?
A)thevoltagedecreases
B)thevoltageincreases
C)thechargedecreases
D)thechargeincreases
E)bothvoltageandchargechange
ConcepTest Varying Capacitance I
Follow-up: How do you increase the charge?
Since,whenthespacingd isdoubled,
thecapacitanceC ishalved.Andsince,thatmeans
thechargemustdecrease.
Q =CΔV
400 V
≝
Oncethebatteryisdisconnected,Q hastoremain
constant,sincenochargecanfloweithertoor
fromthebattery.
Aparallel‐platecapacitorinitiallyhasapotentialdifferenceof400V andisthendisconnectedfromthechargingbattery.Iftheplatespacingisnowdoubled,whatisthenewvalueofthevoltage?
A)100V
B)200V
C)400V
D)800V
E)1600V
+Q –Q
ConcepTest Varying Capacitance II
Since,whenthespacingd isdoubled,
thecapacitanceC ishalved.Andsince ,thatmeansthevoltagemustdouble
400 VQ =CΔV≝
PHYS.1440Lecture10 A.DanylovDepartmentofPhysicsandAppliedPhysics
Thank you
