one is positive, the other is negative both are positive both are negative

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one is positive, the one is positive, the other is negative other is negative both are positive both are positive both are negative both are negative both are positive or both are positive or both are negative both are negative Two charged balls are Two charged balls are repelling each other repelling each other as they hang from the as they hang from the ceiling. What can ceiling. What can you say about their you say about their charges? charges?

description

one is positive, the other is negative both are positive both are negative both are positive or both are negative. Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?. A) have opposite charges - PowerPoint PPT Presentation

Transcript of one is positive, the other is negative both are positive both are negative

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one is positive, the other one is positive, the other

is negative is negative

both are positiveboth are positive

both are negativeboth are negative

both are positive or both both are positive or both

are negativeare negative

Two charged balls are Two charged balls are

repelling each other as repelling each other as

they hang from the ceiling. they hang from the ceiling.

What can you say about What can you say about

their charges?their charges?

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A)A) have opposite chargeshave opposite charges

B) B) have the same chargehave the same charge

C) C) all have the same chargeall have the same charge

D) D) one ball must be neutral (no charge)one ball must be neutral (no charge)

From the picture, From the picture,

what can you what can you

conclude about conclude about

the charges?the charges?

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A) positiveA) positive

B) negativeB) negative

C) positive or neutralC) positive or neutral

D) negative or neutralD) negative or neutral

A metal ball hangs from the ceiling A metal ball hangs from the ceiling

by an insulating thread. The ball is by an insulating thread. The ball is

attractedattracted to a to a positivepositive-charged rod -charged rod

held near the ball. The charge of held near the ball. The charge of

the ball must be:the ball must be:

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Two neutral conductors are connected Two neutral conductors are connected

by a wire and a charged rod is brought by a wire and a charged rod is brought

near, near, butbut does not touchdoes not touch. The wire is . The wire is

taken away, and taken away, and then the charged rod then the charged rod

is removedis removed. What are the charges on . What are the charges on

the conductors?the conductors?

A) 0 0

B) + –

C) – +

D) – –0 0

? ?

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A

B

C

D

E

F

Two uniformly charged spheres are firmly fastened to and Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?magnitude and direction of the electrostatic forces?

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A) 3/4 NA) 3/4 N

B) 3.0 NB) 3.0 N

C) 12 NC) 12 N

D) 16 ND) 16 N

If we increase one charge to If we increase one charge to 4Q4Q, ,

what is the magnitude ofwhat is the magnitude of F F11??

4Q4Q QQF1 = ? F2 = ?

QQ QQF1 = 3N F2 = ?

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A) 9 A) 9 FF

B) 3 B) 3 FF

C) 1/3 C) 1/3 FF

D) 1/9 D) 1/9 FF

The force between two charges The force between two charges

separated by a distance separated by a distance dd is is FF. If . If

the charges are pulled apart to a the charges are pulled apart to a

distance distance 33dd, what is the force on , what is the force on

each charge?each charge?

QQFF

QFF

dd

QQ??

QQ??

33dd

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A) yes, but only if A) yes, but only if QQ00 is positive is positive

B) yes, but only if B) yes, but only if QQ00 is negative is negative

C) yes, independent of the sign C) yes, independent of the sign

(or value) of (or value) of QQ00

D) no, the net force can never D) no, the net force can never

be zerobe zero

Two balls with charges Two balls with charges ++QQ and and +4+4QQ

are fixed at a separation distance are fixed at a separation distance

of of 33RR. Is it possible to place . Is it possible to place

another charged ball another charged ball QQ00 on the line on the line

between the two charges such that between the two charges such that

the net force on the net force on QQ00 will be zero? will be zero?

3R

+Q +4Q

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3R

+Q –– 4Q

Two balls with charges Two balls with charges

++QQ and and –4–4QQ are fixed at are fixed at

a separation distance of a separation distance of

33RR. Is it possible to . Is it possible to

place another charged place another charged

ball ball QQ00 anywhereanywhere on the on the

line such that the net line such that the net

force on force on QQ00 will be will be

zero?zero?

A) yes, but only if A) yes, but only if QQ00 is positive is positive

B) yes, but only if B) yes, but only if QQ00 is negative is negative

C) yes, independent of the sign C) yes, independent of the sign

(or value) of (or value) of QQ00

D) no, the net force can never be D) no, the net force can never be

zerozero

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A proton and an electron are A proton and an electron are

held apart a distance of 1 m held apart a distance of 1 m

and then released. As they and then released. As they

approach each other, what approach each other, what

happens to the force between happens to the force between

them?them?

A) it gets biggerA) it gets bigger

B) it gets smallerB) it gets smaller

C) it stays the same C) it stays the same

p e

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Which of the arrows best Which of the arrows best

represents the direction represents the direction

of the net force on of the net force on

charge +charge +QQ due to the due to the

other two charges?other two charges?+2Q

+4Q

+Q

A BC

Dd

d

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A) 2 A) 2 EE00

B) B) EE00

C) 1/2 C) 1/2 EE00

D) 1/4 D) 1/4 EE00

You are sitting a certain distance You are sitting a certain distance

from a point charge, and you from a point charge, and you

measure an electric field of measure an electric field of EE00. If the . If the

charge is charge is doubleddoubled and your distance and your distance

from the charge is also from the charge is also doubleddoubled, what , what

is the electric field strength now?is the electric field strength now?

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+2 +1+1 +1d d

A)A)

B)B)

C) it’s the same for bothC) it’s the same for both

Between the Between the redred and the and the blueblue

charge, which experiences charge, which experiences

the greater the greater electric fieldelectric field due due

to the to the yellowyellow charge? charge?

+2

+1

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+2 +1+1 +1d d

A) A)

B)B)

C) it’s the same for bothC) it’s the same for both

Between the Between the redred and the and the blueblue

charge, which experiences charge, which experiences

the greater the greater electric forceelectric force due due

to the to the yellowyellow charge? charge?

+2

+1

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Which arrow best Which arrow best

represents the electric represents the electric

field at the center of the field at the center of the

square?square?CB

A

-2 C

-2 C

D) E = 0

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What is the What is the

direction of the direction of the

electric field at the electric field at the

position of the position of the XX ? ?D

CB

A

+Q

-Q +Q

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Field LinesField Lines

Field lines point in the direction of the Field lines point in the direction of the Coulomb force on a positive test charge Coulomb force on a positive test charge due to the charge creating the fielddue to the charge creating the field

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Electric fields add up vectoriallyElectric fields add up vectorially

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Asymmetric charge distribution Asymmetric charge distribution yields asymmetric fieldyields asymmetric field

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Parallel PlatesParallel Plates

•Constant electric field far away from the top and the bottom

•Constant direction•Constant strength

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A) protonA) proton

B) electronB) electron

C) both the same C) both the same

p e

A proton and an electron are held A proton and an electron are held

apart a distance of 1 m and then apart a distance of 1 m and then

released. Which particle has the released. Which particle has the

larger acceleration at any one larger acceleration at any one

moment?moment?

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A proton and an A proton and an

electron are held apart electron are held apart

a distance of 1 m and a distance of 1 m and

then let go. Where then let go. Where

would they meet?would they meet?

A) in the middleA) in the middle

B) closer to the electron’s sideB) closer to the electron’s side

C) closer to the proton’s sideC) closer to the proton’s side

p e

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Flux through an AreaFlux through an Area

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Curved Curved Surface and Surface and non-uniform non-uniform

FieldField

Changing for Changing for every point on every point on surface:surface:– Strength of EStrength of E– Direction of EDirection of E– Direction of ADirection of A

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Angle determines sign of fluxAngle determines sign of flux

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What is the Flux through the What is the Flux through the Surfaces?Surfaces?

A1 pos., A2 negA1 pos., A2 neg

A2 pos., A1 negA2 pos., A1 neg

Both zeroBoth zero

None of the None of the aboveabove

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A gaussian cylinder is placed in a uniform electric A gaussian cylinder is placed in a uniform electric field of magnitude field of magnitude EE, aligned with the cylinder , aligned with the cylinder axis. For each of the surfaces 1, 2, 3, is the axis. For each of the surfaces 1, 2, 3, is the electric flux electric flux

A.A. positive, positive,

B.B. negative, ornegative, or

C.C. zero?zero?

E

123

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A gaussian cylinder encloses a negative charge. A gaussian cylinder encloses a negative charge. For each of the surfaces 1, 2, 3, is the electric flux For each of the surfaces 1, 2, 3, is the electric flux

A.A. positive, positive,

B.B. negative, ornegative, or

C.C. zero?zero?

123

–Q

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A positive charge is located outside a gaussian A positive charge is located outside a gaussian cylinder as shown. For each of the surfaces 1, 2, 3, cylinder as shown. For each of the surfaces 1, 2, 3, is the electric flux is the electric flux

A.A. positive, positive,

B.B. negative, ornegative, or

C.C. zero?zero?

123

+Q

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Which statement do you agree with? Which statement do you agree with? A.A. ““Since each Gaussian surface encloses the same charge, the net Since each Gaussian surface encloses the same charge, the net

flux through each should be the same.”flux through each should be the same.”B.B. ““Gauss’s law doesn’t apply here. The electric field at the Gaussian Gauss’s law doesn’t apply here. The electric field at the Gaussian

surface in case B is weaker than in case A, because the surface is surface in case B is weaker than in case A, because the surface is farther from the charge. Since the flux is proportional to the electric farther from the charge. Since the flux is proportional to the electric field strength, the flux must also be smaller in case B.”field strength, the flux must also be smaller in case B.”

C.C. ““I was comparing A and C. In C the charge outside the Gaussian I was comparing A and C. In C the charge outside the Gaussian surface changes the field over the whole surface. The areas are surface changes the field over the whole surface. The areas are the same so the fluxes must be different.”the same so the fluxes must be different.”

D.D. None of these statements is correct.None of these statements is correct.

+Q

A B C

+Q+Q

-6Q

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Gauss’s law problem solvingGauss’s law problem solving

1.1. Symmetry of charge distributions Symmetry of charge distributions Gaussian Gaussian surfacesurface

2.2. Draw Gaussian surface through point where you Draw Gaussian surface through point where you want to know E fieldwant to know E field

3.3. Determine direction of E field from symmetry of Determine direction of E field from symmetry of charge distributioncharge distribution

4.4. Calculate electric flux through Gaussian surfaceCalculate electric flux through Gaussian surface

5.5. Calculate charge enclosed by surfaceCalculate charge enclosed by surface

6.6. Solve for E as a function of distance from charge Solve for E as a function of distance from charge using Gauss’ lawusing Gauss’ law

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What is the symmetry of a long What is the symmetry of a long straight wire with line charge straight wire with line charge

density density λλ??

CylindricalCylindrical

EllipticalElliptical

SphericalSpherical

PlanarPlanar

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What is the symmetry of a non-What is the symmetry of a non-conducting conducting hollowhollow sphere with sphere with

charge density charge density ρρ??

CylindricalCylindrical

EllipticalElliptical

SphericalSpherical

PlanarPlanar

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Which Gaussian surface should we Which Gaussian surface should we choose to calculate the electric field choose to calculate the electric field of a non-conducting hollow sphere of a non-conducting hollow sphere

with charge density with charge density ρρ ? ?CylinderCylinder

PillboxPillbox

SphereSphere

OtherOther

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Which radius should the Gaussian Which radius should the Gaussian sphere of a non-conducting hollow sphere of a non-conducting hollow sphere with charge density sphere with charge density ρρ have? have?

Less than inner radius of hollow sphere Less than inner radius of hollow sphere

More than outer radius of hollow sphereMore than outer radius of hollow sphere

Between inner and outer radius of hollow Between inner and outer radius of hollow sphere sphere

Depends on where you are interested in Depends on where you are interested in the electric fieldthe electric field

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Which is the symmetry of a sheet of Which is the symmetry of a sheet of metal with surface charge density metal with surface charge density

σσ??

CylindricalCylindrical

EllipticalElliptical

SphericalSpherical

PlanarPlanar

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Which Gaussian surface should we Which Gaussian surface should we choose to calculate the electric field choose to calculate the electric field

of a metal sheet with surface of a metal sheet with surface charge density charge density σσ??

CylinderCylinder

PillboxPillbox

SphereSphere

OtherOther

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Which of the three surfaces of the Which of the three surfaces of the pillbox has a non-zero electric flux?pillbox has a non-zero electric flux?

Top (outside conductor)Top (outside conductor)

Mantle (half-submerged)Mantle (half-submerged)

BottomBottom

All threeAll three

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Electric field of a solid charged Electric field of a solid charged spheresphere

Choose gaussian Choose gaussian surface Asurface A1 1 to to

calculate E field calculate E field outsideoutside sphere sphere

Choose gaussian Choose gaussian surface Asurface A2 2 to to

calculate E field calculate E field insideinside sphere sphere

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Electric field of solid charged Electric field of solid charged spheresphere

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How does the electric field of a long How does the electric field of a long wire depend on R?wire depend on R?

Not, Const.Not, Const.

RR

1/R1/R

1/R1/R22

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Non-conducting solid cylinder and cylindrical Non-conducting solid cylinder and cylindrical tube, both carry charge density 15tube, both carry charge density 15μμC/mC/m33; ;

RR11=1/2R=1/2R22=R=R33/3=5cm. Calculate the electric field./3=5cm. Calculate the electric field.

Group 1: inside Group 1: inside solid cylindersolid cylinder

Group 2: between Group 2: between cylinderscylinders

Group 3: inside Group 3: inside hollow cylinderhollow cylinder

Group 4: outside Group 4: outside both cylinders both cylinders

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Electric Field as a function of Electric Field as a function of distance from axisdistance from axis

0.0

2.0

4.0

6.0

8.0

10.0

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

R (cm)

E (

104 N

/C)

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The analogy of the potential energy The analogy of the potential energy of two rocks are charges between of two rocks are charges between

charged plates. Which plate should charged plates. Which plate should be on top?be on top?

Positive Positive

NegativeNegative

DependsDepends

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The analogy of the potential energy The analogy of the potential energy of two rocks are charges between of two rocks are charges between

charged plates. What does the charged plates. What does the small rock represent?small rock represent?

More chargeMore charge

Less chargeLess charge

Negative chargeNegative charge

DependsDepends

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The analogy of the potential energy The analogy of the potential energy of two rocks are charges between of two rocks are charges between charged plates. What is a correct charged plates. What is a correct

analogy?analogy?

Neg. plates up and neg. Neg. plates up and neg. charges highcharges highNeg. plates down and neg. Neg. plates down and neg. charges highcharges highPos. plates and neg. Pos. plates and neg. charges up/highcharges up/highNone of the aboveNone of the above

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What is correct?What is correct?

Potential would be lower at b for negative Potential would be lower at b for negative chargescharges

The potential at b is higher for the larger chargeThe potential at b is higher for the larger charge

Negative charges go from low to high potentialNegative charges go from low to high potential

None of the aboveNone of the above

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A proton is moved from position A proton is moved from position ii to position to position f f below. Is the change in its below. Is the change in its potential potential energyenergy

A.A. positive,positive,

B.B. negative, ornegative, or

C.C. zero?zero?

+ i f

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In each of the situations shown below, an electron In each of the situations shown below, an electron is moved from position is moved from position ii to position to position ff. Is the . Is the change in its change in its potential energypotential energy

A.A. positive,positive,B.B. negative, ornegative, orC.C. zero?zero?

+ i f

3.

i f

1.

+ -

2.

i

f

+ -

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+ -

Draw the field lines & equipotential lines of two Draw the field lines & equipotential lines of two

charges platescharges plates

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Draw the field lines & equipotential lines of Draw the field lines & equipotential lines of

a point charge a point charge

+

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Draw the field lines & equipotential lines of Draw the field lines & equipotential lines of

two opposite point charges two opposite point charges

+ --

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Draw the field lines & equipotential lines of Draw the field lines & equipotential lines of

two point charges two point charges

+ +

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Four point charges are Four point charges are

arranged at the corners of a arranged at the corners of a

square. square.

Draw the field lines & Draw the field lines &

equipotential linesequipotential lines

--QQ

--QQ ++QQ

++QQ

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Four point charges are arranged Four point charges are arranged

at the corners of a square. What at the corners of a square. What

are the are the electric field electric field EE and and

potential potential VV at the at the center of the center of the

square? Draw the field lines & square? Draw the field lines &

equipotential linesequipotential lines

A) E = 0 V = 0

B) E = 0 V 0

C) E 0 V 0

D) E 0 V = 0

--QQ

--QQ ++QQ

++QQ

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The electric potential is shown at four The electric potential is shown at four points in space below. Estimate the points in space below. Estimate the electric field (magnitude and direction!) at electric field (magnitude and direction!) at the dot.the dot.

25 V

10 V

10 V

15 V

?E

7.1mm

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An electron is shot directly towards a 2mm An electron is shot directly towards a 2mm diameter plastic bead with charge –1 nC diameter plastic bead with charge –1 nC from very far away. It “reflects” from the from very far away. It “reflects” from the bead reaching a turning point 1mm from bead reaching a turning point 1mm from the surface of the bead. What was the the surface of the bead. What was the initial speed of the electron?initial speed of the electron?

-1 nC

1mm

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The potential of a point charge Q is The potential of a point charge Q is assessed at different distances. Sort assessed at different distances. Sort

the potential starting from the highest.the potential starting from the highest.A) V 1cm in front of Q=+2nCA) V 1cm in front of Q=+2nCB) V 1m behind Q=+2nCB) V 1m behind Q=+2nCC) V 1cm left of Q=-4nCC) V 1cm left of Q=-4nCD) V 1m right of Q=-4nCD) V 1m right of Q=-4nC

ABCDABCDABDCABDCDCBADCBANone of the aboveNone of the above

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Equipotential LinesEquipotential Lines

Electric field is perpendicular Electric field is perpendicular to equipotential linesto equipotential lines– Does this determine its Does this determine its

direction fully?direction fully?– Why is the right plate at 0V?Why is the right plate at 0V?

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Point Point chargecharge

Can we Can we calculate calculate how big the how big the charge is?charge is?

Is it positive Is it positive or negative?or negative?

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What What would a would a negative negative charge charge

change?change?Shape of Shape of equipotential equipotential lineslinesPotentials Potentials would be would be negativenegativePotential would Potential would increase from increase from centercenterotherother

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Do the distorted circles on the left Do the distorted circles on the left represent the same potential as the represent the same potential as the

right ones?right ones?

NoNo

YesYes

Up to a Up to a signsign

DependsDepends

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A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage separated by a distance d. A battery with voltage V is connected across the plates. For each V is connected across the plates. For each modification listed, state whether the modification listed, state whether the capacitancecapacitance A) increasesA) increases, , B) decreasesB) decreases, or , or C) stays the sameC) stays the same..

1.1. Increase dIncrease d

2.2. Increase AIncrease A

3.3. Increase VIncrease V

4.4. Reverse battery polarityReverse battery polarity

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A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage separated by a distance d. A battery with voltage V is connected across the plates. For each V is connected across the plates. For each modification listed, state whether the modification listed, state whether the capacitancecapacitance A) increasesA) increases, , B) decreasesB) decreases, or , or C) stays the sameC) stays the same..

1.1. Increase d Increase d C= C=εε00 A/d A/d C decreases C decreases2.2. Increase A Increase A C= C=εε00 A/d A/d C increases C increases3.3. Increase V Increase V C not function of V C not function of V (device (device

does not change)does not change) C same C same Note that charge goes up (Q=CV at constant C), Note that charge goes up (Q=CV at constant C),

so electric field goes up (E= so electric field goes up (E= εε00 Q/A for plate of Q/A for plate of charges) [yet it is constant as a function of charges) [yet it is constant as a function of position!], which is, of course, why the potential position!], which is, of course, why the potential difference (V=Ed at constant d) is up. difference (V=Ed at constant d) is up.

4.4. Reverse battery polarity Reverse battery polarity same, device same, device does not changedoes not change

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A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage separated by a distance d. A battery with voltage V is connected across the plates. For each of the V is connected across the plates. For each of the following modifications, state whether the following modifications, state whether the charge charge on the plate connected to the positive battery on the plate connected to the positive battery terminalterminal A) increasesA) increases, , B) decreasesB) decreases, or , or C) stays C) stays the same.the same.

1.1. Increase d Increase d

2.2. Increase AIncrease A

3.3. Increase VIncrease V

4.4. Reverse battery polarityReverse battery polarity

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A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage separated by a distance d. A battery with voltage V is connected across the plates. For each of the V is connected across the plates. For each of the following modifications, state whether the following modifications, state whether the charge charge on the plate connected to the positive battery on the plate connected to the positive battery terminalterminal A) increasesA) increases, , B) decreasesB) decreases, or , or C) stays C) stays the same.the same.

1.1. Increase d Increase d V=const. (same battery), C= V=const. (same battery), C=εε00 A/d decreases A/d decreases Q=CV decreases Q=CV decreases

2.2. Increase AIncrease A V=const. (same battery), C= V=const. (same battery), C=εε00 A/d increases A/d increases Q=CV increases Q=CV increases

3.3. Increase V Increase V C=const., so Q=CV increases C=const., so Q=CV increases4.4. Reverse battery polarity: Reverse battery polarity: Reversing polarity Reversing polarity

will first decrease charge, so that charge will first decrease charge, so that charge built-up is opposite later.built-up is opposite later.

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A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with potential separated by a distance d. A battery with potential difference V is connected across the plates for a difference V is connected across the plates for a long time, and then disconnected. For each of the long time, and then disconnected. For each of the following modifications, state whether the following modifications, state whether the potential difference between the platespotential difference between the plates A) A) increasesincreases, , B) decreasesB) decreases, or , or C) stays the sameC) stays the same..

1.1. Increase dIncrease d

2.2. Increase AIncrease A

Page 68: one is positive, the other is negative  both are positive both are negative

A parallel plate capacitor has plates with area A, A parallel plate capacitor has plates with area A, separated by a distance d. A battery with potential separated by a distance d. A battery with potential difference V is connected across the plates for a difference V is connected across the plates for a long time, and then disconnected. For each of the long time, and then disconnected. For each of the following modifications, state whether the following modifications, state whether the potential difference between the platespotential difference between the plates A) A) increasesincreases, , B) decreasesB) decreases, or , or C) stays the sameC) stays the same..

1.1. Increase d Increase d Q=const., C decreases Q=const., C decreases V=Q/C increases (more voltage needed for V=Q/C increases (more voltage needed for same charge)same charge)

2.2. Increase AIncrease A Q=const., C increases Q=const., C increases V=Q/C decreases (less voltage needed to V=Q/C decreases (less voltage needed to keep same charge)keep same charge)

Page 69: one is positive, the other is negative  both are positive both are negative

Consider a simple parallel-plate capacitor whose Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and plates are given equal and opposite charges and are separated by a distance are separated by a distance dd. Suppose the . Suppose the plates are pulled apart until they are separated by plates are pulled apart until they are separated by a distance a distance DD > > dd. The . The electrostatic energyelectrostatic energy stored stored in the capacitor is nowin the capacitor is now

A.A. greater than greater than

B.B. the same as the same as

C.C. smaller than smaller than

before the plates were pulled apart.before the plates were pulled apart.

Page 70: one is positive, the other is negative  both are positive both are negative

Consider a simple parallel-plate capacitor whose Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and plates are given equal and opposite charges and are separated by a distance are separated by a distance dd. Suppose the . Suppose the plates are pulled apart until they are separated by plates are pulled apart until they are separated by a distance a distance DD > > dd. The . The electrostatic energyelectrostatic energy stored stored in the capacitor is nowin the capacitor is now

A.A. greater than greater than

B.B. the same as the same as

C.C. smaller than smaller than

before the plates were pulled apart.before the plates were pulled apart.

Q=const here, so if d is increased, device Q=const here, so if d is increased, device changes changes C goes down, V goes up, U=1/2 QV C goes down, V goes up, U=1/2 QV goes up.goes up.

Page 71: one is positive, the other is negative  both are positive both are negative

Consider a simple parallel-plate capacitor which Consider a simple parallel-plate capacitor which has been fully charged by a battery with potential has been fully charged by a battery with potential V and left connected to it. Suppose the plates V and left connected to it. Suppose the plates are pulled apart from their initial separation are pulled apart from their initial separation dd to a to a separation separation DD > > dd. The . The electrostatic energyelectrostatic energy stored stored in the capacitor is nowin the capacitor is now

A.A. greater thangreater than

B.B. the same as the same as

C.C. smaller than smaller than

before the plates were pulled apart.before the plates were pulled apart.

Page 72: one is positive, the other is negative  both are positive both are negative

Consider a simple parallel-plate capacitor which Consider a simple parallel-plate capacitor which has been fully charged by a battery with potential V has been fully charged by a battery with potential V and left connected to it. Suppose the plates are and left connected to it. Suppose the plates are pulled apart from their initial separation pulled apart from their initial separation dd to a to a separation separation DD > > dd. The . The electrostatic energyelectrostatic energy stored in stored in the capacitor is nowthe capacitor is now

A.A. greater thangreater than

B.B. the same as the same as

C.C. smaller than smaller than

before the plates were pulled apart.before the plates were pulled apart.

Now V=const, charge Q can change. C goes down, Now V=const, charge Q can change. C goes down, so Q=CV goes down, so U=1/2 QV goes down.so Q=CV goes down, so U=1/2 QV goes down.