Physics for Scientists & Engineers 2

Size: px
Start display at page:

Download "Physics for Scientists & Engineers 2"

Transcription

1 Capacitors Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 12 Capacitors are evices that can store electrical energy Capacitors are use in many every-ay applications Heart efibrillators Camera flash units Capacitors are an integral part of moern ay electronics Capacitors an be micro-size on computer chips or super-size for high power circuits such as FM raio transmitters February 2, 2005 Physics for Scientists&Engineers 2 1 February 2, 2005 Physics for Scientists&Engineers 2 2 Capacitance Parallel Plate Capacitor Capacitors come in a variety of sizes an shapes However, in general, a capacitor consists of two separate conuctors, usually calle plates, even if these conuctors are not simple planes We will start our stuy of capacitors by efining a convenient geometry an generalize from there We will start with a capacitor consisting of two parallel conucting planes, each with area A separate by a istance We assume that these plates are in a vacuum (air is very close to a vacuum) We call this evice a parallel plate capacitor +q q We charge the capacitor by placing a charge +q on the top plate a charge -q on the bottom plate Because the plates are conuctors, the charge will istribute itself evenly over the surface of the conucting plates The electric potential, V, is proportional to the amount of charge on the plates February 2, 2005 Physics for Scientists&Engineers 2 3 February 2, 2005 Physics for Scientists&Engineers 2 4 1

2 Parallel Plate Capacitor (2) +q q Definition of Capacitance The efinition of capacitance is C = q V The proportionality constant between the charge q an the electric potential ifference V is the capacitance C q = CV We will call the electric potential ifference V the potential or the voltage between the plates The capacitance of a evice epens on the area of the plates an the istance between the plates, but oes not epen on the voltage across the plates or the charge on the plates The capacitance of a evice tells us how much charge is require to prouce a given voltage across the plates February 2, 2005 Physics for Scientists&Engineers 2 5 The units of capacitance are coulombs per volt The unit of capacitance has been given the name fara (abbreviate F) name after British physicist Michael Faraay ( ) 1 F = 1 C 1 V A fara is a very large capacitance Typically we eal with µf (10-6 F), nf (10-9 F), or pf (10-12 F) February 2, 2005 Physics for Scientists&Engineers 2 6 Charging/Discharging a Capacitor Charging/Discharging a Capacitor (2) We can charge a capacitor by connecting the capacitor to a battery or to a power supply A battery or power supply is esigne to supply charge at a given voltage When we connect a capacitor to a battery, charge flows from the battery until the capacitor is fully charge If we then isconnect the battery or power supply, the capacitor will retain its charge an voltage A real-life capacitor will leak charge, but here we will assume ieal capacitors that hol their charge an voltage inefinitely February 2, 2005 Physics for Scientists&Engineers 2 7 Let s illustrate the charging processing using a circuit iagram In the circuit iagram Lines represent conuctors The battery or power supply is represente by The capacitor is represente by the symbol This circuit has a switch When the switch is between positions a an b, the circuit is open (not connecte) When the switch is in position a, the battery is connecte across the capacitor When the switch is in position b, the two plates of the capacitor are connecte Charge will flow between the plates an the capacitor will ischarge February 2, 2005 Physics for Scientists&Engineers 2 8 2

3 Parallel Plate Capacitor Parallel Plate Capacitor (2) Consier two parallel conucting plates separate by a istance We can calculate the electric fiel between the plates using Gauss Law 0 " Ei A = q We take a Gaussian surface shown by the re ashe line This arrangement is calle a parallel plate capacitor The upper plate has +q an the lower plate has -q The electric fiel between the plates points from the positively charge plate to the negatively charge plate We will assume ieal parallel plate capacitors in which the electric fiel is constant between the plates an zero elsewhere Real-life capacitors have fringe fiel near the eges The electric fiel is zero insie the conuctor so the top part of the Gaussian surface oes not contribute to the integral The vertical parts of the Gaussian surface o not contribute because the electric fiel is zero outsie the capacitor The only contribution to the integral comes from the Gaussian surface insie the constant electric fiel of the capacitor February 2, 2005 Physics for Scientists&Engineers 2 9 February 2, 2005 Physics for Scientists&Engineers 2 10 Parallel Plate Capacitor (3) Parallel Plate Capacitor (4) We then get the electric fiel E insie the parallel plate capacitor to be 0 EA = q Now we calculate the electric potential across the plates of the capacitor in terms of the electric fiel f V = " Ei s # i We efine the electric potential across the capacitor to be V an we carry out the integral in the irection of the blue arrow The integral gives us V = E Remembering the efinition of capacitance C = q V We get the result for the capacitance of a parallel plate capacitor Where C = 0 A A is the area of each plate is the istance between the plates Note that this result for the capacitance of a parallel plate capacitor epens only on the geometry of the capacitor an not on the amount of charge or the voltage across the capacitor February 2, 2005 Physics for Scientists&Engineers 2 11 February 2, 2005 Physics for Scientists&Engineers

4 Example - Capacitance of a Parallel Plate Capacitor Example 2 - Capacitance of a Parallel Plate Capacitor We have a parallel plate capacitor constructe of two parallel plates, each with area 625 cm 2 separate by a istance of 1.00 mm. What is the capacitance of this parallel plate capacitor? C = 0A A = 625 cm 2 = m 2 = 1.00 mm = 1.00 "10 #3 m ( )( m 2 ) C = 8.85 "10#12 F/m 1.00 "10 #3 m C = nf = 5.53"10-10 F A parallel plate capacitor constructe out of square conucting plates 25 cm x 25 cm separate by 1 mm prouces a capacitor with a capacitance of about 0.5 nf We have a parallel plate capacitor constructe of two parallel plates separate by a istance of 1.00 mm. What area is require to prouce a capacitance of 1.00 F? C = 0A = 1.00 mm = 1.00 "10 #3 m A = C = 0 ( 1.00 "10 #3 m) ( 1.00 F) ( 8.85 "10 #12 F/m) = 1.13"10 8 m 2 A parallel plate capacitor constructe out of square conucting plates 10.6 km x 10.6 km (6 miles x 6 miles) separate by 1 mm prouces a capacitor with a capacitance of 1 F February 2, 2005 Physics for Scientists&Engineers 2 13 February 2, 2005 Physics for Scientists&Engineers 2 14 Cylinrical Capacitor Cylinrical Capacitor (2) Consier a capacitor constructe of two collinear conucting cyliners of length L The inner cyliner has raius an the outer cyliner has raius r 2 Both cyliners have charge per unit length λ with the inner cyliner having positive charge an the outer cyliner having negative charge We will assume an ieal cylinrical capacitor The electric fiel points raially from the inner cyliner to the outer cyliner The electric fiel is zero outsie the collinear cyliners We can apply Gauss Law to get the electric fiel between the two cyliner using a Gaussian surface in the for of a cyliner with raius r an length L as illustrate by the re lines 0 "$ Ei A = 0 EA = 0 E( 2"r) L = q = #L Which we can rewrite to get an expression for the electric fiel between the two cyliners E = 2"# 0 r February 2, 2005 Physics for Scientists&Engineers 2 15 February 2, 2005 Physics for Scientists&Engineers

5 Cylinrical Capacitor (3) As we i for the parallel plate capacitor, we efine the voltage ifference across the two cyliners to be V, which we obtain by integrating from the negatively charge cyliner to the positively charge cyliner " V = Er = r 2 2#$ 0 r r = " % ln r ( 2 r 2 2#$ 0 & ' ) * The capacitance of a cylinrical capacitor is C = q V = L ln r 2 / 2"# 0 ( ) = 2"# L 0 ln( r 2 / ) February 2, 2005 Physics for Scientists&Engineers 2 17 Example - Capacitance of a Coaxial Cable Assume that we have a 20.0 m long coaxial cable compose of a conuctor an a coaxial shiel aroun the conuctor. The raius of the conuctor is mm an the raius of the shiel is 2.00 mm. What is the capacitance of the coaxial cable? We can think of the conuctor of the cable as a cyliner because all the charge will resie on the surface of the conuctor The capacitance of the cable is C = 2" 0L ln r 2 / ( ) L = 20.0 m = mm = "4 m r 2 = 2.00 mm = "3 m ( ) 2" C = m ln 2.00 #10 $3 m / 2.5 #10 $4 m ( ) = 5.35 #10-10 F = nf February 2, 2005 Physics for Scientists&Engineers

Potential from a distribution of charges = 1

Potential from a distribution of charges = 1 Lecture 7 Potential from a distribution of charges V = 1 4 0 X Smooth distribution i q i r i V = 1 4 0 X i q i r i = 1 4 0 Z r dv Calculating the electric potential from a group of point charges is usually

More information

Physics Electricity & Op-cs Lecture 8 Chapter 24 sec Fall 2017 Semester Professor

Physics Electricity & Op-cs Lecture 8 Chapter 24 sec Fall 2017 Semester Professor Physics 24100 Electricity & Op-cs Lecture 8 Chapter 24 sec. 1-2 Fall 2017 Semester Professor Kol@ck How Much Energy? V 1 V 2 Consider two conductors with electric potentials V 1 and V 2 We can always pick

More information

CAPACITANCE: CHAPTER 24. ELECTROSTATIC ENERGY and CAPACITANCE. Capacitance and capacitors Storage of electrical energy. + Example: A charged spherical

CAPACITANCE: CHAPTER 24. ELECTROSTATIC ENERGY and CAPACITANCE. Capacitance and capacitors Storage of electrical energy. + Example: A charged spherical CAPACITANCE: CHAPTER 24 ELECTROSTATIC ENERGY an CAPACITANCE Capacitance an capacitors Storage of electrical energy Energy ensity of an electric fiel Combinations of capacitors In parallel In series Dielectrics

More information

UNIT 4:Capacitors and Dielectric

UNIT 4:Capacitors and Dielectric UNIT 4:apacitors an Dielectric SF7 4. apacitor A capacitor is a evice that is capable of storing electric charges or electric potential energy. It is consist of two conucting plates separate by a small

More information

Goal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics.

Goal of this chapter is to learn what is Capacitance, its role in electronic circuit, and the role of dielectrics. PHYS 220, Engineering Physics, Chapter 24 Capacitance an Dielectrics Instructor: TeYu Chien Department of Physics an stronomy University of Wyoming Goal of this chapter is to learn what is Capacitance,

More information

1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity

1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A soli conucting sphere is given a positive charge Q.

More information

Second Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of 2.77 µf. What is C 2?

Second Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of 2.77 µf. What is C 2? Secon Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of.77 µf. What is C? C 4.0 µf.0 µf A) 7 µf B) µf C) 4 µf D) 3 µf E) 6 µf Q. When the potential ifference across

More information

( ) Energy storage in CAPACITORs. q C

( ) Energy storage in CAPACITORs. q C Energy storage in CAPACITORs Charge capacitor by transferring bits of charge q at a time from bottom to top plate. Can use a battery to o this. Battery oes work which increase potential energy of capacitor.

More information

PHYS 221 General Physics II

PHYS 221 General Physics II PHYS 221 General Physics II Capacitance, Dielectrics, Lightning Spring 2015 Assigne Reaing: 18.4 18.6 Lecture 5 Recap: PHYS 221 Last Lecture Electric force is conservative Electric potential energy Potential

More information

Capacitance and capacitors. Dr. Loai Afana

Capacitance and capacitors. Dr. Loai Afana apacitance and capacitors apacitors apacitors are devices that store energy in an electric field. apacitors are used in many every-day applications Heart defibrillators amera flash units apacitors are

More information

It's often useful to find all the points in a diagram that have the same voltage. E.g., consider a capacitor again.

It's often useful to find all the points in a diagram that have the same voltage. E.g., consider a capacitor again. 17-7 (SJP, Phys 22, Sp ') It's often useful to fin all the points in a iagram that have the same voltage. E.g., consier a capacitor again. V is high here V is in between, here V is low here Everywhere

More information

PARALLEL-PLATE CAPACITATOR

PARALLEL-PLATE CAPACITATOR Physics Department Electric an Magnetism Laboratory PARALLEL-PLATE CAPACITATOR 1. Goal. The goal of this practice is the stuy of the electric fiel an electric potential insie a parallelplate capacitor.

More information

Electrostatics: Capacitor Examples

Electrostatics: Capacitor Examples Electrostatics: apacitor Examples EE3321 Electromagnetic Fiel Theory Outline Parallel plate capacitor How big is a Fara? oaxial capacitor RG-59 coax Inhomogeneous capacitor Electrostatics -- apacitor Examples

More information

From last time. Attention. Capacitance. Spherical capacitor. Energy stored in capacitors. How do we charge a capacitor? Today:

From last time. Attention. Capacitance. Spherical capacitor. Energy stored in capacitors. How do we charge a capacitor? Today: Attention From last time More on electric potential an connection to Efiel How to calculate Efiel from V Capacitors an Capacitance switch off computers in the room an be prepare to a very lou noise Toay:

More information

Phys102 Second Major-122 Zero Version Coordinator: Sunaidi Sunday, April 21, 2013 Page: 1

Phys102 Second Major-122 Zero Version Coordinator: Sunaidi Sunday, April 21, 2013 Page: 1 Coorinator: Sunaii Sunay, April 1, 013 Page: 1 Q1. Two ientical conucting spheres A an B carry eual charge Q, an are separate by a istance much larger than their iameters. Initially the electrostatic force

More information

iclicker A device has a charge q=10 nc and a potential V=100V, what s its capacitance? A: 0.1 nf B: 1nF C: 10nF D: F E: 1F

iclicker A device has a charge q=10 nc and a potential V=100V, what s its capacitance? A: 0.1 nf B: 1nF C: 10nF D: F E: 1F Lecture 8 iclicker A device has a charge q=10 nc and a potential V=100V, what s its capacitance? A: 0.1 nf B: 1nF C: 10nF D: 10 10 F E: 1F iclicker A device has a charge q=10 nc and a potential V=100V,

More information

CHAPTER: 2 ELECTROSTATIC POTENTIAL AND CAPACITANCE

CHAPTER: 2 ELECTROSTATIC POTENTIAL AND CAPACITANCE CHAPTER: 2 ELECTROSTATIC POTENTIAL AND CAPACITANCE. Define electric potential at a point. *Electric potential at a point is efine as the work one to bring a unit positive charge from infinity to that point.

More information

anubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics

anubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics anubhavclasses.worpress.com CBSE Solve Test Papers PHYSICS Class XII Chapter : Electrostatics anubhavclasses.worpress.com CBSE TEST PAPER-05 CLASS - XII PHYSICS (Unit Electrostatics). The Plates of a charge

More information

Electricity & Optics

Electricity & Optics Physics 24100 Electricity & Optics Lecture 9 Chapter 24 sec. 3-5 Fall 2017 Semester Professor Koltick Parallel Plate Capacitor Area, A C = ε 0A Two Parallel Plate Capacitors Area, A 1 C 1 = ε 0A 1 Area,

More information

Electrical apacity Synopsis Electrical apacity i) Electrical capacity of a conuctor is its ability to store electric charge i The potential acuire by a conuctor is irectly proportional to the charge given

More information

Q1. A) 3F/8 B) F/4 C) F/2 D) F/16 E) F The charge on A will be Q 2. Ans: The charge on B will be 3 4 Q. F = k a Q r 2. = 3 8 k Q2 r 2 = 3 8 F

Q1. A) 3F/8 B) F/4 C) F/2 D) F/16 E) F The charge on A will be Q 2. Ans: The charge on B will be 3 4 Q. F = k a Q r 2. = 3 8 k Q2 r 2 = 3 8 F Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 1 Q1. Two ientical conucting spheres A an B carry eual charge Q, an are separate by a istance much larger than their iameters.

More information

1. An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement:

1. An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement: Chapter 24: ELECTRIC POTENTIAL 1 An electron moves from point i to point f, in the irection of a uniform electric fiel During this isplacement: i f E A the work one by the fiel is positive an the potential

More information

1/7/2018. A model of the mechanism for electrostatic interactions. GRAVITATIONAL FORCE vs. ELECTROSTATCS FORCE OBJECT WITH MASS

1/7/2018. A model of the mechanism for electrostatic interactions. GRAVITATIONAL FORCE vs. ELECTROSTATCS FORCE OBJECT WITH MASS UNIT 3 Electrostatics: electric force, electric fiel, an electric potential. CHAPTER 15 THE ELECTRIC FIELD AP PHYSICS A moel of the mechanism for electrostatic interactions A moel for electric interactions,

More information

Physics 219 Question 1 January

Physics 219 Question 1 January Lecture 6-16 Physics 219 Question 1 January 30. 2012. A (non-ideal) battery of emf 1.5 V and internal resistance 5 Ω is connected to a light bulb of resistance 50 Ω. How much power is delivered to the

More information

Where A is the plate area and d is the plate separation.

Where A is the plate area and d is the plate separation. DIELECTRICS Dielectrics an the parallel plate capacitor When a ielectric is place between the plates of a capacitor is larger for the same value of voltage. From the relation C = /V it can be seen that

More information

Get Solution of These Packages & Learn by Video Tutorials on

Get Solution of These Packages & Learn by Video Tutorials on Get Solution of These Packages & Learn by Vieo Tutorials on www.mathsbysuhag.com FREE Downloa Stuy Package from website: www.tekolasses.com & www.mathsbysuhag.com. INTRODUTION APAIT ITANE A capacitor can

More information

PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR

PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR PRACTICE 4. CHARGING AND DISCHARGING A CAPACITOR. THE PARALLEL-PLATE CAPACITOR. The Parallel plate capacitor is a evice mae up by two conuctor parallel plates with total influence between them (the surface

More information

Electric Potential. Slide 1 / 29. Slide 2 / 29. Slide 3 / 29. Slide 4 / 29. Slide 6 / 29. Slide 5 / 29. Work done in a Uniform Electric Field

Electric Potential. Slide 1 / 29. Slide 2 / 29. Slide 3 / 29. Slide 4 / 29. Slide 6 / 29. Slide 5 / 29. Work done in a Uniform Electric Field Slie 1 / 29 Slie 2 / 29 lectric Potential Slie 3 / 29 Work one in a Uniform lectric Fiel Slie 4 / 29 Work one in a Uniform lectric Fiel point a point b The path which the particle follows through the uniform

More information

PH 132 Exam 1 Spring Student Name. Student Number. Lab/Recitation Section Number (11,,36)

PH 132 Exam 1 Spring Student Name. Student Number. Lab/Recitation Section Number (11,,36) PH 13 Exam 1 Spring 010 Stuent Name Stuent Number ab/ecitation Section Number (11,,36) Instructions: 1. Fill out all of the information requeste above. Write your name on each page.. Clearly inicate your

More information

ECE341 Test 2 Your Name: Tue 11/20/2018

ECE341 Test 2 Your Name: Tue 11/20/2018 ECE341 Test Your Name: Tue 11/0/018 Problem 1 (1 The center of a soli ielectric sphere with raius R is at the origin of the coorinate. The ielectric constant of the sphere is. The sphere is homogeneously

More information

Today s agenda: Capacitors and Capacitance. You must be able to apply the equation C=Q/V.

Today s agenda: Capacitors and Capacitance. You must be able to apply the equation C=Q/V. Today s agenda: Capacitors and Capacitance. You must be able to apply the equation C=Q/V. Capacitors: parallel plate, cylindrical, spherical. You must be able to calculate the capacitance of capacitors

More information

Chapter 24 Capacitance and Dielectrics

Chapter 24 Capacitance and Dielectrics Chapter 24 Capacitance and Dielectrics 1 Capacitors and Capacitance A capacitor is a device that stores electric potential energy and electric charge. The simplest construction of a capacitor is two parallel

More information

qq 1 1 q (a) -q (b) -2q (c)

qq 1 1 q (a) -q (b) -2q (c) 1... Multiple Choice uestions with One Correct Choice A hollow metal sphere of raius 5 cm is charge such that the potential on its surface to 1 V. The potential at the centre of the sphere is (a) zero

More information

Chapter 4. Electrostatics of Macroscopic Media

Chapter 4. Electrostatics of Macroscopic Media Chapter 4. Electrostatics of Macroscopic Meia 4.1 Multipole Expansion Approximate potentials at large istances 3 x' x' (x') x x' x x Fig 4.1 We consier the potential in the far-fiel region (see Fig. 4.1

More information

5-4 Electrostatic Boundary Value Problems

5-4 Electrostatic Boundary Value Problems 11/8/4 Section 54 Electrostatic Bounary Value Problems blank 1/ 5-4 Electrostatic Bounary Value Problems Reaing Assignment: pp. 149-157 Q: A: We must solve ifferential equations, an apply bounary conitions

More information

Capacitance and Dielectrics

Capacitance and Dielectrics 6 Capacitance an Dielectrics CHAPTER OUTLINE 6. Definition of Capacitance 6. Calculating Capacitance 6.3 Combinations of Capacitors 6.4 Energy Store in a Charge Capacitor 6.5 Capacitors with Dielectrics

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Electromagnetic Oscillations Physics for Scientists & Engineers Spring Semester 005 Lecture 8! We have been working with circuits that have a constant current a current that increases to a constant current

More information

Physics 2212 K Quiz #2 Solutions Summer 2016

Physics 2212 K Quiz #2 Solutions Summer 2016 Physics 1 K Quiz # Solutions Summer 016 I. (18 points) A positron has the same mass as an electron, but has opposite charge. Consier a positron an an electron at rest, separate by a istance = 1.0 nm. What

More information

Chapter 17 ELECTRIC POTENTIAL

Chapter 17 ELECTRIC POTENTIAL Chapter 17 ELECTRIC POTENTIAL Conceptual Questions 1. (a) The electric fiel oes positive work on q as it moves closer to +Q. (b) The potential increases as q moves closer to +Q. (c) The potential energy

More information

Capacitors. January 2002 Number 29

Capacitors. January 2002 Number 29 PhysicsFactsheet January 22 Number 29 Capacitors Introuction Capacitors are wiely use in electrical engineering an electronics hey are important in any physics course because of the variety of uses they

More information

Physics 2212 GJ Quiz #4 Solutions Fall 2015

Physics 2212 GJ Quiz #4 Solutions Fall 2015 Physics 2212 GJ Quiz #4 Solutions Fall 215 I. (17 points) The magnetic fiel at point P ue to a current through the wire is 5. µt into the page. The curve portion of the wire is a semicircle of raius 2.

More information

2013 Feb 13 Exam 1 Physics 106. Physical Constants:

2013 Feb 13 Exam 1 Physics 106. Physical Constants: 203 Feb 3 xam Physics 06 Physical onstants: proton charge = e =.60 0 9 proton mass = m p =.67 0 27 kg electron mass = m e = 9. 0 3 kg oulomb constant = k = 9 0 9 N m 2 / 2 permittivity = ǫ 0 = 8.85 0 2

More information

Chapter 24 Capacitance and Dielectrics

Chapter 24 Capacitance and Dielectrics Chapter 24 Capacitance and Dielectrics 1 Capacitors and Capacitance A capacitor is a device that stores electric potential energy and electric charge. The simplest construction of a capacitor is two parallel

More information

Designing Information Devices and Systems I Spring 2017 Official Lecture Notes Note 13

Designing Information Devices and Systems I Spring 2017 Official Lecture Notes Note 13 EES 6A Designing Information Devices an Systems I Spring 27 Official Lecture Notes Note 3 Touchscreen Revisite We ve seen how a resistive touchscreen works by using the concept of voltage iviers. Essentially,

More information

1. An electron moves from point i to point f, in the direction of a uniform electric eld. During this displacement: ² ² i

1. An electron moves from point i to point f, in the direction of a uniform electric eld. During this displacement: ² ² i Chapter 24: ELECTRIC POTENTIAL 1 An electron moves from point i to point f, in the irection of a uniform electric el During this isplacement: ² ² i f ~E A the work one by the el is positive an the potential

More information

Chapter 26 - Capacitance

Chapter 26 - Capacitance Chapter 26 Capacitance Probem Set #5 ue: Ch 26 2, 3, 5, 7, 9, 5, 22, 26, 29, 6, 63, 64 The ieas of energy storage in fies can be carrie a step further by unerstaning the concept of "Capacitance." Lecture

More information

A capcitor is a divice which stores electric energy. It is also named as condenser.

A capcitor is a divice which stores electric energy. It is also named as condenser. PITNE PITNE. capcitor is a ivice which stores electric energy. It is also name as conenser. When charge is given to a conuctor, its potential increases in the ratio of given charge. The charge given to

More information

iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed?

iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed? 1 iclicker A metal ball of radius R has a charge q. Charge is changed q -> - 2q. How does it s capacitance changed? q A: C->2 C0 B: C-> C0 C: C-> C0/2 D: C->- C0 E: C->-2 C0 2 iclicker A metal ball of

More information

Energy Stored in Capacitors

Energy Stored in Capacitors Energy Stored in Capacitors U = 1 2 qv q = CV U = 1 2 CV 2 q 2 or U = 1 2 C 37 Energy Density in Capacitors (1) We define the, u, as the electric potential energy per unit volume Taking the ideal case

More information

Capacitance: The ability to store separated charge C=Q/V. Capacitors! Capacitor. Capacitance Practice SPH4UW 24/08/2010 Q = CV

Capacitance: The ability to store separated charge C=Q/V. Capacitors! Capacitor. Capacitance Practice SPH4UW 24/08/2010 Q = CV SPH4UW Capacitors! Capacitance: The ability to store separate charge C=Q/V Charge Q on plates V = V V B = E 0 Charge 2Q on plates V = V V B =2E 0 E=E 0 B E=2E 0 B Physics 102: Lecture 4, Slie 1 Potential

More information

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 16

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 16 EECS 16A Designing Information Devices an Systems I Spring 218 Lecture Notes Note 16 16.1 Touchscreen Revisite We ve seen how a resistive touchscreen works by using the concept of voltage iviers. Essentially,

More information

TEST 2 (PHY 250) Figure Figure P26.21

TEST 2 (PHY 250) Figure Figure P26.21 TEST 2 (PHY 250) 1. a) Write the efinition (in a full sentence) of electric potential. b) What is a capacitor? c) Relate the electric torque, exerte on a molecule in a uniform electric fiel, with the ipole

More information

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions

AP Physics C: Electricity and Magnetism 2004 Free-Response Questions AP Physics C: Electricity an Magnetism 004 Free-Response Questions The materials inclue in these files are intene for noncommercial use by AP teachers for course an exam preparation; permission for any

More information

Friday July 11. Reminder Put Microphone On

Friday July 11. Reminder Put Microphone On Friday July 11 8:30 AM 9:0 AM Catch up Lecture 3 Slide 5 Electron projected in electric field problem Chapter 23 Problem 29 Cylindrical shell problem surrounding wire Show Faraday Ice Pail no chrage inside

More information

Physics 505 Electricity and Magnetism Fall 2003 Prof. G. Raithel. Problem Set 3. 2 (x x ) 2 + (y y ) 2 + (z + z ) 2

Physics 505 Electricity and Magnetism Fall 2003 Prof. G. Raithel. Problem Set 3. 2 (x x ) 2 + (y y ) 2 + (z + z ) 2 Physics 505 Electricity an Magnetism Fall 003 Prof. G. Raithel Problem Set 3 Problem.7 5 Points a): Green s function: Using cartesian coorinates x = (x, y, z), it is G(x, x ) = 1 (x x ) + (y y ) + (z z

More information

Our next test will be on Tuesday, March 14

Our next test will be on Tuesday, March 14 Physics 2212G/H Test form Name Spring 2017 Test 2 Recitation Section (see back of test): 1) Print your name, test form number (above), an nine- igit stuent number in the section of the answer car labele

More information

ABCD42BEF F2 F8 5 4D658 CC89

ABCD42BEF F2 F8 5 4D658 CC89 ABCD BEF F F D CC Vetri Velan GSI, Physics 7B Miterm 2: Problem Solution. Outsie sphere, E looks like a point charge. E = The total charge on the sphere is Q sphere = ρ 4 3 πr3 Thus, outsie the sphere,

More information

Chapter 6. Electromagnetic Oscillations and Alternating Current

Chapter 6. Electromagnetic Oscillations and Alternating Current hapter 6 Electromagnetic Oscillations an Alternating urrent hapter 6: Electromagnetic Oscillations an Alternating urrent (hapter 31, 3 in textbook) 6.1. Oscillations 6.. The Electrical Mechanical Analogy

More information

Homework 7 Due 18 November at 6:00 pm

Homework 7 Due 18 November at 6:00 pm Homework 7 Due 18 November at 6:00 pm 1. Maxwell s Equations Quasi-statics o a An air core, N turn, cylinrical solenoi of length an raius a, carries a current I Io cos t. a. Using Ampere s Law, etermine

More information

Maxwell s Equations 5/9/2016. EELE 3332 Electromagnetic II Chapter 9. Maxwell s Equations for static fields. Review Electrostatics and Magnetostatics

Maxwell s Equations 5/9/2016. EELE 3332 Electromagnetic II Chapter 9. Maxwell s Equations for static fields. Review Electrostatics and Magnetostatics Generate by Foxit PDF Creator Foxit oftware 5/9/216 3332 lectromagnetic II Chapter 9 Maxwell s quations Islamic University of Gaza lectrical ngineering Department Prof. Dr. Hala J l-khozonar 216 1 2 Review

More information

Physics Jonathan Dowling. Physics 2102 Lecture 7 Capacitors I

Physics Jonathan Dowling. Physics 2102 Lecture 7 Capacitors I Physics 2102 Jonathan Dowling Physics 2102 Lecture 7 Capacitors I Capacitors and Capacitance Capacitor: any two conductors, one with charge +, other with charge Potential DIFFERENCE etween conductors =

More information

shown in Fig. 4, is initially uncharged. How much energy is stored in the two capacitors after the switch S is closed for long time?

shown in Fig. 4, is initially uncharged. How much energy is stored in the two capacitors after the switch S is closed for long time? Chapter 25 Term 083 Q13. Each of the two 25-µF capacitors, as shown in Fig. 3, is initially uncharged. How many Coulombs of charge pass through ammeter A after the switch S is closed for long time? A)

More information

Chapter 24 Capacitance and Dielectrics

Chapter 24 Capacitance and Dielectrics Chapter 24 Capacitance and Dielectrics Lecture by Dr. Hebin Li Goals for Chapter 24 To understand capacitors and calculate capacitance To analyze networks of capacitors To calculate the energy stored in

More information

PHY 114 Summer 2009 Final Exam Solutions

PHY 114 Summer 2009 Final Exam Solutions PHY 4 Summer 009 Final Exam Solutions Conceptual Question : A spherical rubber balloon has a charge uniformly istribute over its surface As the balloon is inflate, how oes the electric fiel E vary (a)

More information

General Physics ph 213 Midterm Exam II (Ch 24 27) November 14, False, they don t have to be flat but they must be perpendicular to E-field.

General Physics ph 213 Midterm Exam II (Ch 24 27) November 14, False, they don t have to be flat but they must be perpendicular to E-field. General Phsics ph 13 Miterm am II Ch 7 November 1, 005 Name: Tpe am is close boo an close notes. Use onl our note car. Write all wor an answers in the papers provie. Show all our wor an eplain our reasoning

More information

Capacitance and Dielectrics

Capacitance and Dielectrics Slide 1 / 39 Capacitance and Dielectrics 2011 by Bryan Pflueger Capacitors Slide 2 / 39 A capacitor is any two conductors seperated by an insulator, such as air or another material. Each conductor has

More information

Alpha Particle scattering

Alpha Particle scattering Introuction Alpha Particle scattering Revise Jan. 11, 014 In this lab you will stuy the interaction of α-particles ( 4 He) with matter, in particular energy loss an elastic scattering from a gol target

More information

8.022 (E&M) Lecture 19

8.022 (E&M) Lecture 19 8. (E&M) Lecture 19 Topics: The missing term in Maxwell s equation Displacement current: what it is, why it s useful The complete Maxwell s equations An their solution in vacuum: EM waves Maxwell s equations

More information

(3-3) = (Gauss s law) (3-6)

(3-3) = (Gauss s law) (3-6) tatic Electric Fiels Electrostatics is the stuy of the effects of electric charges at rest, an the static electric fiels, which are cause by stationary electric charges. In the euctive approach, few funamental

More information

Capacitance, Resistance, DC Circuits

Capacitance, Resistance, DC Circuits This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple

More information

Chapter 25. Capacitance

Chapter 25. Capacitance Chapter 25 Capacitance 1 1. Capacitors A capacitor is a twoterminal device that stores electric energy. 2 2. Capacitance The figure shows the basic elements of any capacitor two isolated conductors of

More information

Prep 1. Oregon State University PH 213 Spring Term Suggested finish date: Monday, April 9

Prep 1. Oregon State University PH 213 Spring Term Suggested finish date: Monday, April 9 Oregon State University PH 213 Spring Term 2018 Prep 1 Suggeste finish ate: Monay, April 9 The formats (type, length, scope) of these Prep problems have been purposely create to closely parallel those

More information

12.11 Laplace s Equation in Cylindrical and

12.11 Laplace s Equation in Cylindrical and SEC. 2. Laplace s Equation in Cylinrical an Spherical Coorinates. Potential 593 2. Laplace s Equation in Cylinrical an Spherical Coorinates. Potential One of the most important PDEs in physics an engineering

More information

CHAPTER 18 ELECTRIC POTENTIAL

CHAPTER 18 ELECTRIC POTENTIAL CHAPTER 18 ELECTRIC POTENTIAL BASIC CONCEPTS: ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ELECTRIC POTENTIAL GRADIENT POTENTIAL DIFFERENCE POTENTIAL ENERGY 1 h PE = U = mgh Or PE U KE K And U + K = total

More information

Electric Potential & Potential Energy

Electric Potential & Potential Energy Electric Potential & Potential Energy I) ELECTRIC POTENTIAL ENERGY of a POINT CHARGE Okay, remember from your Mechanics: Potential Energy (U) is gaine when you o work against a fiel (like lifting a weight,

More information

University Physics (PHY 2326)

University Physics (PHY 2326) Chapter 23 University Physics (PHY 2326) Lecture 5 Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors 3/26/2015

More information

Chapter 24: Capacitance and Dielectrics

Chapter 24: Capacitance and Dielectrics Chapter 24: Capacitance and Dielectrics When you compress/stretch a spring, we are storing potential energy This is the mechanical method to store energy It is also possible to store electric energy as

More information

Chapter 24: Capacitance and Dielectrics

Chapter 24: Capacitance and Dielectrics Chapter 24: Capacitance and Dielectrics When you compress/stretch a spring, we are storing potential energy This is the mechanical method to store energy It is also possible to store electric energy as

More information

Direct Current (DC) Circuits

Direct Current (DC) Circuits Direct Current (DC) Circuits NOTE: There are short answer analysis questions in the Participation section the informal lab report. emember to include these answers in your lab notebook as they will be

More information

Moving Charges And Magnetism

Moving Charges And Magnetism AIND SINGH ACADEMY Moving Charges An Magnetism Solution of NCET Exercise Q -.: A circular coil of wire consisting of turns, each of raius 8. cm carries a current of. A. What is the magnitue of the magnetic

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 2140) Lecture 5 Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors http://www.physics.wayne.edu/~apetrov/phy2140/

More information

Electronics Capacitors

Electronics Capacitors Electronics Capacitors Wilfrid Laurier University October 9, 2015 Capacitor an electronic device which consists of two conductive plates separated by an insulator Capacitor an electronic device which consists

More information

Solution to Quiz 2. April 18, 2010

Solution to Quiz 2. April 18, 2010 Solution to Quiz April 8, 00 Four capacitors are connected as shown below What is the equivalent capacitance of the combination between points a and b? a µf b 50 µf c 0 µf d 5 µf e 34 µf Answer: b (A lazy

More information

Lecture XII. where Φ is called the potential function. Let us introduce spherical coordinates defined through the relations

Lecture XII. where Φ is called the potential function. Let us introduce spherical coordinates defined through the relations Lecture XII Abstract We introuce the Laplace equation in spherical coorinates an apply the metho of separation of variables to solve it. This will generate three linear orinary secon orer ifferential equations:

More information

CURRENT ELECTRICITY Q.1

CURRENT ELECTRICITY Q.1 CUENT EECTCTY Q. Define Electric current an its unit.. Electric Current t can be efine as the time rate of flow of charge in a conuctor is calle Electric Current. The amount of flow of charge Q per unit

More information

Capacitors And Dielectrics

Capacitors And Dielectrics 1 In this small e-book we ll learn about capacitors and dielectrics in short and then we ll have some questions discussed along with their solutions. I ll also give you a practices test series which you

More information

6. The total charge will be conserved, and the final potential difference across the capacitors will be the same. Q Q Q Q C C C + C C C

6. The total charge will be conserved, and the final potential difference across the capacitors will be the same. Q Q Q Q C C C + C C C Homework for the week of October. 4th week of classes. h. 4: 6, 5, 8, 7, 9,, 4, 44, 49, 58, 6 h. 5: 7, 8, 9 6. The total charge will be conserve, an the final potential ifference across the capacitors

More information

Chapter 25. Capacitance

Chapter 25. Capacitance Chapter 25 Capacitance 25.2: Capacitance: 25.2: Capacitance: When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: q+ and q-. However, we refer to the charge of a

More information

Conductors & Capacitance

Conductors & Capacitance Conuctors & Capacitance PICK UP YOUR EXAM;; Average of the three classes is approximately 51. Stanar eviation is 18. It may go up (or own) by a point or two once all graing is finishe. Exam KEY is poste

More information

Potentials and Fields

Potentials and Fields Potentials and Fields Review: Definition of Potential Potential is defined as potential energy per unit charge. Since change in potential energy is work done, this means V E x dx and E x dv dx etc. The

More information

A-level PHYSICS A PHYA4/1. Unit 4 Fields and Further Mechanics. Section A. Monday 20 June 2016 Morning

A-level PHYSICS A PHYA4/1. Unit 4 Fields and Further Mechanics. Section A. Monday 20 June 2016 Morning Please write clearly in block capitals. entre number aniate number Surname Forename(s) aniate signature -level PHYSIS Unit 4 Fiels an Further Mechanics Section Monay 20 June 2016 Morning Materials In aition

More information

V q.. REASONING The potential V created by a point charge q at a spot that is located at a

V q.. REASONING The potential V created by a point charge q at a spot that is located at a 8. REASONING The electric potential at a istance r from a point charge q is given by Equation 9.6 as kq / r. The total electric potential at location P ue to the four point charges is the algebraic sum

More information

Capacitor: any two conductors, one with charge +Q, other with charge -Q Potential DIFFERENCE between conductors = V

Capacitor: any two conductors, one with charge +Q, other with charge -Q Potential DIFFERENCE between conductors = V Physics 2102 Gabriela González Capacitor: any two conductors, one with charge +Q, other with charge -Q Potential DIFFERENCE between conductors = V Units of capacitance: Farad (F) = Coulomb/Volt -Q +Q Uses:

More information

Physics 202, Exam 1 Review

Physics 202, Exam 1 Review Physics 202, Exam 1 Review Logistics Topics: Electrostatics + Capacitors (Chapters 21-24) Point charges: electric force, field, potential energy, and potential Distributions: electric field, electric potential.

More information

Last Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor.

Last Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor. Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge ccumultes

More information

';:::::'*n':,:#;':,":!::*:,::"'if atttheshett'scharge

';:::::'*n':,:#;':,:!::*:,::'if atttheshett'scharge Ouestions ' ber. A gamma ruy entere the chamber from the bottom an at one point transforme into an electron an a positron. Because those new particles were charge an moving, each left a trail of tiny bubbles.

More information

Physics 42 Exam 2 PRACTICE Name: Lab

Physics 42 Exam 2 PRACTICE Name: Lab Physics 42 Exam 2 PRACTICE Name: Lab 1 2 3 4 Conceptual Multiple Choice (2 points each) Circle the best answer. 1.Rank in order, from brightest to dimmest, the identical bulbs A to D. A. C = D > B > A

More information

Capacitance and Dielectrics

Capacitance and Dielectrics 3/30/05 apacitance an Dielectrics Goals of this Lecture To unerstan capacitors an calculate capacitance To analyze networks of capacitors To calculate the enery store in a capacitor To examine ielectrics

More information

Capacitance and Dielectrics

Capacitance and Dielectrics Chapter 24 Capacitance and Dielectrics PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 24 To understand capacitors

More information

Chapter 17. Potential and Capacitance

Chapter 17. Potential and Capacitance Chapter 17 Potential and Capacitance Potential Voltage (potential) is the analogue of water pressure while current is the analogue of flow of water in say gal/min or Kg/s Think of a potential as the words

More information