Physics II Chapter 26Department of Physics and Applied Physics Today we are going to discuss:...

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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/

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

Connecting Potential and Field (Review)

sdEVVVf

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.

dxdVEx

ConcepTest My Favorite question

The Geometry of Potential and Field

Let s be along an equipotential line, dsdVEs

where V=const. So dV=0. dsdVEs

0So, it is impossible to have an electric field along equipotential lines,

linesialequipotentE

equipotential lines

Whichsetofequipotentialsurfacesmatchesthiselectricfield?

ConcepTest Geometry E and V

Potential of a Conductor

sdEVVVf

0V if VV

Aconductorinelectrostaticequilibriumisatthesamepotential.

constV

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

CapacitorstoresenergyAcapacitorisasystemthatstorespotentialenergyinaformofanelectricfield.

Ugh!It’s just energy

Capacitor

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:

Parallel-plate capacitor

In its simplest form, a capacitor consists of a pair of parallel metal plates separated by air/insulating material.

Let’sfindcapacitanceofaparallel‐platecapacitor

Capacitanceisapurelygeometricpropertyoftwoelectrodesbecauseitdependsonlyontheirsurfaceareaandspacing.

+Q–Q

Theelectricfieldbetweentheplatesisη ‐ surfacechargedensity

(Eq.25.26)Thepotentialdifferencebetweenplates:

WeneedtofindQandΔV:

Thisgivesthecapacitance:

WecanincreasecapacitancebyincreasingareaAbymaking“arollofmetalandinsulator”

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

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≝

Thank you

Physics II Chapter 26Department of Physics and Applied Physics Today we are going to discuss:...

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