electrostatics ct solution

8/13/2019 Electrostatics CT Solution

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ConcepTest PowerPoints

(hapter )*

Physics: Principles with

Applications, 6 th edition

+iancoli



ConcepTest 16.1aConcepTest 16.1a ,lectric (harge -,lectric (harge -

)% one is positive. the other

is negative

2% both are positive

/% both are negative

% both are positive or both

are negative

Two charged balls areTwo charged balls are

repelling each other asrepelling each other as

they hang fro" the ceilingthey hang fro" the ceiling

$hat can you say about$hat can you say about

their charges1their charges1



ConcepTest 16.1aConcepTest 16.1a ,lectric (harge -,lectric (harge -

The fact that the balls repel each

other only can tell you that they

have the sa"e chargesa"e charge. but you do

not know the sign So they can

be either both positive or both

negative

)% one is positive. the other

is negative

2% both are positive

/% both are negative

% both are positive or both

are negative

Two charged balls areTwo charged balls are

repelling each other asrepelling each other as

they hang fro" the ceilingthey hang fro" the ceiling

$hat can you say about$hat can you say about

their charges1their charges1

ollow3up4ollow3up4 $hat does the picture look like if the two balls are oppositely$hat does the picture look like if the two balls are oppositelycharged1 $hat about if both balls are neutral1charged1 $hat about if both balls are neutral1



)% have opposite charges

2% have the sa"e charge

/% all have the sa"e charge

% one ball "ust be neutral #no charge%

ro" the picture.ro" the picture.

what can youwhat can you

conclude aboutconclude about

the charges1the charges1

ConcepTest 16.1bConcepTest 16.1b ,lectric (harge --,lectric (harge --



)% have opposite charges

2% have the sa"e charge

/% all have the sa"e charge

% one ball "ust be neutral #no charge%

ro" the picture.ro" the picture.

what can youwhat can you

conclude aboutconclude about

the charges1the charges1

The +,,6 and P-67 balls "ust

have the sa"e charge. since they

repel each other The 8,99:$

ball also repels the +,,6. so it

"ust also have the sa"e charge

as the +,,6 #and the P-67%

ConcepTest 16.1bConcepTest 16.1b ,lectric (harge --,lectric (harge --



ConcepTest 16.2aConcepTest 16.2a (onductors -(onductors -

)% positive

2% negative/% neutral

% positive or neutral

5% negative or neutral

' "etal ball hangs fro" the ceiling

by an insulating thread The ball is

attracted to a positive3charged rod

held near the ball The charge of

the ball "ust be4



(learly. the ball will be attracted if its

charge is negativenegative However. even if

the ball is neutralneutral. the charges in theball can be separated by inductioninduction

#polari;ation%. leading to a net

attraction

)% positive

2% negative/% neutral

% positive or neutral

5% negative or neutral

' "etal ball hangs fro" the ceiling

by an insulating thread The ball is

attracted to a positive3charged rod

held near the ball The charge of

the ball "ust be4

re"e"berthe ball is aconductor<

ConcepTest 16.2aConcepTest 16.2a (onductors -(onductors -

ollow3up4ollow3up4 $hat happens if the$hat happens if the "etal ball"etal ball is replaced by ais replaced by a plastic ballplastic ball11



Two neutral conductors are connected

by a wire and a charged rod is brought

near. but does not touch The wire is

taken away. and then the charged rod

is re"oved $hat are the charges on

the conductors1

ConcepTest 16.2bConcepTest 16.2b (onductors --(onductors --

)% 0 0

2% = >

/% > =

% = =

5% > >

0 0

1 1



$hile the conductors are connected. positivepositive

charge will flow fro" the blue to the greencharge will flow fro" the blue to the green

ball due to polari;ationball due to polari;ation :nce disconnected.

the charges will re"ain on the separatecharges will re"ain on the separate

conductorsconductors even when the rod is re"oved

Two neutral conductors are connected

by a wire and a charged rod is brought

near. but does not touch The wire is

taken away. and then the charged rod

is re"oved $hat are the charges on

the conductors1

ConcepTest 16.2bConcepTest 16.2b (onductors --(onductors --

)% 0 0

2% = >

/% > =

% = =

5% > >

0 0

1 1

ollow3up4ollow3up4 $hat will happen when the$hat will happen when the

conductors are reconnected with a wire1conductors are reconnected with a wire1



?? ??F ) @ /6 F 2 @ 1

)% )0 6

2% )5 6/% 20 6

% /0 6

5% *0 6

$hat is the "agnitude$hat is the "agnitude

of the force of the force 2211

ConcepTest 16.3aConcepTest 16.3a (oulo"bAs 9aw -(oulo"bAs 9aw -



The force F 2 "ust have the same manitudesame manitude as F ) This is

due to the fact that the for" of (oulo"bAs 9aw is totally

sy""etric with respect to the two charges involved The

force of one on the other of a pair is the sa"e as the reverseforce of one on the other of a pair is the sa"e as the reverse

6ote that this sounds suspiciously like 6ewtonAs /rd 9aw<<6ote that this sounds suspiciously like 6ewtonAs /rd 9aw<<

?? ??F ) @ /6 F 2 @ 1

)% )0 6

2% )5 6/% 20 6

% /0 6

5% *0 6

$hat is the "agnitude$hat is the "agnitude

of the forceof the force F F 2211

ConcepTest 16.3aConcepTest 16.3a (oulo"bAs 9aw -(oulo"bAs 9aw -



ConcepTest 16.3bConcepTest 16.3b (oulo"bAs 9aw --(oulo"bAs 9aw --

)% /B 6

2% /0 6

/% )2 6

% )* 6

5% C 6

-f we increase one charge to-f we increase one charge to

??. what is the "agnitude of . what is the "agnitude of

F F ))11

?? ??

F ) @ 1 F 2 @ 1

?? ??F ) @ /6 F 2 @ 1



ConcepTest 16.3bConcepTest 16.3b (oulo"bAs 9aw --(oulo"bAs 9aw --

:riginally we had4

F ) @ !"#$"#$%r 2 @ / 6

6ow we have4

F ) @ !"&#$"#$%r 2

which is ti"es bigger ti"es bigger than before

)% /B 6

2% /0 6

/% )2 6

% )* 6

5% C 6

-f we increase one charge to-f we increase one charge to

??. what is the "agnitude of. what is the "agnitude of

F F ))11

# # # #

F ) @ 1 F 2 @ 1

# # # # F ) @ /6 F 2 @ 1

ollow3up4ollow3up4 6ow what is the "agnitude of6ow what is the "agnitude of F F 2211



)% D F

2% / F

/% F

% )B/ F

5% )BD F

The force between two charges

separated by a distance d is F -f

the charges are pulled apart to a

distance /d . what is the force on

each charge1

??F F

?F F

d d

??11

??11

//d d

ConcepTest 16.3c ConcepTest 16.3c (oulo"bAs 9aw ---(oulo"bAs 9aw ---



:riginally we had4

F before @ !"#$"#$%d 2 @ F

6ow we have4

F after @ !"#$"#$%"3d$2 @ )BD F

)% D F

2% / F

/% F

% )B/ F

5% )BD F

The force between two charges

separated by a distance d is F -f

the charges are pulled apart to a

distance /d . what is the force on

each charge1

??F F

?F F

d d

??11

??11

//d d

ConcepTest 16.3c ConcepTest 16.3c (oulo"bAs 9aw ---(oulo"bAs 9aw ---

ollow3up4ollow3up4 $hat is the force if the original distance is halved1 $hat is the force if the original distance is halved1



ConcepTest 16.&aConcepTest 16.&a ,lectric orce -,lectric orce -

)% yes. but only if # # 00 is positiveis positive

2% yes. but only if # # 00 is negativeis negative/% yes. independent of the sign

#or value% of # # 00

% no. the net force can never

be ;ero

Two balls with chargesTwo balls with charges ==# # andand ==# #

are fi&ed at a separation distanceare fi&ed at a separation distance

ofof //' ' -s it possible to place -s it possible to place

another charged ballanother charged ball # # 00 on the lineon the line

between the two charges such thatbetween the two charges such that

the net force onthe net force on # # 00 will be ;ero1will be ;ero1

/'

=# =#



ConcepTest 16.&aConcepTest 16.&a ,lectric orce -,lectric orce -

)% yes. but only if # # 00 is positiveis positive

2% yes. but only if # # 00 is negativeis negative/% yes. independent of the sign

#or value% of # # 00

% no. the net force can never

be ;ero

Two balls with chargesTwo balls with charges ==# # andand ==# #

are fi&ed at a separation distanceare fi&ed at a separation distance

ofof //' ' -s it possible to place -s it possible to place

another charged ballanother charged ball # # 00 on the lineon the line

between the two charges such thatbetween the two charges such that

the net force onthe net force on # # 00 will be ;ero1will be ;ero1

/'

=# =#

' positive charge would be repelled

by both charges. so a point where

these two repulsive forces cancel

can be found ' negative charge

would be attracted by both. and the

sa"e argu"ent holds

ollow3up4ollow3up4 $hat happens if both charges are = $hat happens if both charges are =# # 11$here would the$here would the F F @ 0 point be in this case1@ 0 point be in this case1



Two balls with chargesTwo balls with charges ==# # andand ==# # are separated byare separated by //' ' $here $here

should you place another charged ballshould you place another charged ball # # 00 on the line between theon the line between the

two charges such that the net force ontwo charges such that the net force on # # 00 will be ;ero1will be ;ero1

/'

=# =#

' 2'

) 2 / 5

ConcepTest 16.&bConcepTest 16.&b ,lectric orce --,lectric orce --



Two balls with chargesTwo balls with charges ==# # andand ==# # are separated byare separated by //' ' $here $here

should you place another charged ballshould you place another charged ball # # 00 on the line between theon the line between the

two charges such that the net force ontwo charges such that the net force on # # 00 will be ;ero1will be ;ero1

The force on # 0 due to =# is4 F @ !"# ( $"#$%'

2

The force on # 0 due to =# is4 F @ !"# ( $"&#$%"2'$2

Since =# is ti"es bigger than =# . then # 0 needs to be

farther fro" =# -n fact. # 0 "ust be twice as far fro" =# .since the distance is s uared in (oulo"bAs 9aw

/'

=# =#

' 2'

) 2 / 5

ConcepTest 16.&bConcepTest 16.&b ,lectric orce --,lectric orce --



' proton and an electron are

held apart a distance of ) "and then released 's they

approach each other. what

happens to the force between

the"1

)% it gets bigger

2% it gets s"aller

/% it stays the sa"e

p e

ConcepTest 16.*aConcepTest 16.*a Proton and ,lectron -Proton and ,lectron -



Fy (oulo"bAs 9aw. the force between theforce between the

two charges is inversely proportional totwo charges is inversely proportional to

the distance sEuaredthe distance sEuared So. the closer they

get to each other. the bigger the electric

force between the" gets<

' proton and an electron are

held apart a distance of ) "and then released 's they

approach each other. what

happens to the force between

the"1

)% it gets bigger

2% it gets s"aller

/% it stays the sa"e

2

21

r

QQk F

p e

ConcepTest 16.*aConcepTest 16.*a Proton and ,lectron -Proton and ,lectron -

ollow3up4ollow3up4 $hich particle feels the larger force at any one "o"ent1 $hich particle feels the larger force at any one "o"ent1



)% proton

2% electron

/% both the sa"e

p e

ConcepTest 16.*bConcepTest 16.*b Proton and ,lectron --Proton and ,lectron --

' proton and an electron are held

apart a distance of ) " and then

released $hich particle has the

larger acceleration at any one

"o"ent1



The two particles feel the sa"e forcesa"e force

Since F + ma. the particle with the s"allers"aller

"ass"ass will have the larger accelerationlarger acceleration

This would be the electronThis would be the electron

)% proton

2% electron

/% both the sa"e

2

21

r

QQk F

p e

ConcepTest 16.*bConcepTest 16.*b Proton and ,lectron --Proton and ,lectron --

' proton and an electron are held

apart a distance of ) " and then

released $hich particle has the

larger acceleration at any one

"o"ent1



' proton and an electron

are held apart a distance

of ) " and then let go

$here would they "eet1

)% in the "iddle2% closer to the electronAs side

/% closer to the protonAs side

p e

ConcepTest 16.*c ConcepTest 16.*c Proton and ,lectron ---Proton and ,lectron ---



Fy 6ewtonAs /rd 9aw. the electron and proton

feel the sa"e forcesa"e force Fut. since F + ma. and

since the protonAs "ass is "uch greater protonAs "ass is "uch greater . the

protonAs acceleration will be "uch s"aller protonAs acceleration will be "uch s"aller <

Thus. they will "eet closer to the protonAscloser to the protonAs

original positionoriginal position

' proton and an electron

are held apart a distance

of ) " and then let go

$here would they "eet1

)% in the "iddle2% closer to the electronAs side

/% closer to the protonAs side

p e

ConcepTest 16.*c ConcepTest 16.*c Proton and ,lectron ---Proton and ,lectron ---

ollow3up4ollow3up4

$hich particle will be "oving faster when they "eet1 $hich particle will be "oving faster when they "eet1

)



$hich of the arrows best

represents the directionof the net force on charge

=# due to the other two

charges1

=2#

=#

=#

) 2

/

5d

d

ConcepTest 16.6 ConcepTest 16.6 orces in 2!orces in 2!

)



The charge =2# repels =# towards

the right The charge =# repels =#

upwards. but with a stronger force

Therefore. the net force is up and tonet force is up and to

the right. but "ostly upthe right. but "ostly up

=2#

=#

=#

) 2

/

5d

d

=2#

=#

ConcepTest 16.6 ConcepTest 16.6 orces in 2!orces in 2!

$hich of the arrows best

represents the directionof the net force on charge

=# due to the other two

charges1

ollow3up4ollow3up4 $hat happens if the$hat happens if theyellow charge would be =/yellow charge would be =/# # 11



#)% 00

#2%22

00

#/% 00

#% )B2)B2 00

#5% )B 00

8ou are sitting a certain distance fro" 8ou are sitting a certain distance fro"

a point charge. and you "easure ana point charge. and you "easure an

electric field ofelectric field of 00 -f the charge is -f the charge is

doubleddoubled and your distance fro" theand your distance fro" the

charge is alsocharge is also doubleddoubled. what is the. what is the

electric field strength now1electric field strength now1

ConcepTest 16.- ConcepTest 16.- ,lectric ield,lectric ield



e"e"ber that the electric field is4 @ !#%r 2

!oubling the charge!oubling the charge puts a factor of 2factor of 2 in the

nu"erator. but doubling the distancedoubling the distance puts a factorfactorof of in the deno"inator. because it is distance

sEuared<< :verall. that gives us a factor of )B2factor of )B2

#)% 00

#2%22

00

#/% 00

#% )B2)B2 00

#5% )B 00

8ou are sitting a certain distance fro" 8ou are sitting a certain distance fro"

a point charge. and you "easure ana point charge. and you "easure an

electric field ofelectric field of 00 -f the charge is -f the charge is

doubleddoubled and your distance fro" theand your distance fro" the

charge is alsocharge is also doubleddoubled. what is the. what is the

electric field strength now1electric field strength now1

ConcepTest 16.- ConcepTest 16.- ,lectric ield,lectric ield

ollow3up4ollow3up4 -f your distance is doubled. what "ust you do to-f your distance is doubled. what "ust you do tothe charge tothe charge to "aintain the sa"e"aintain the sa"e fieldfield at your new position1at your new position1



=2 =)=) =)d d

)%

2%

/% the sa"e for both

Fetween the red and the

blue charge. which of

the" e&periences the

greater electric )ield due

to the green charge1

ConcepTest 16.aConcepTest 16.a ield and orce -ield and orce -

=2

=)



Foth charges feel the sa"e electricsa"e electric

fieldfield due to the green charge because

they are at the sa"e point in spacesa"e point in space<

=2 =)=) =)d d

)%

2%


2r

Qk E =




greater electric )ield due


ConcepTest 16.aConcepTest 16.a ield and orce -ield and orce -

=2

=)



=2 =)=) =)d d

)%

2%





greater electric )orce due


ConcepTest 16.bConcepTest 16.b ield and orce --ield and orce --

=2

=)



The electric field is the sa"eelectric field is the sa"e for both charges.

but the forceforce on a given charge also depends

on the "agnitude of that specific charge"agnitude of that specific charge

=2 =)=) =)d d

)%

2%





greater electric )orce due


qE F =

ConcepTest 16.bConcepTest 16.b ield and orce --ield and orce --

=2

=)

C T 16 / S i i -



$hat is the electric field at$hat is the electric field at

the center of the sEuare1the center of the sEuare1

/

2 )

32 (

32 (

5% @ 0

ConcepTest 16./aConcepTest 16./a Superposition -Superposition -

C T t 16 / S iti -



or the upper charge. the field vector at the center

of the sEuare points towards that charge or the

lower charge. the sa"e thing is true Then the vectorsu" of these two field vectors points to the leftpoints to the left



/

2 )

32 (

32 (

5% @ 0

ConcepTest 16./aConcepTest 16./a Superposition -Superposition -

ollow3up4ollow3up4 $hat if the lower charge was =2 (1$hat if the lower charge was =2 (1

$hat if both charges were =2 (1 $hat if both charges were =2 (1

C T 16 /bC T t 16 /b S i i --S iti --



/

2 )

32 (

32 ( 32 (

32 (

ConcepTest 16./bConcepTest 16./b Superposition --Superposition --



5% @ 0

C T t 16 /bC T t 16 /b S iti --S iti --



The four field vectors all point outwards

fro" the center of the sEuare toward their

respective charges Fecause they are all

eEual. the netnet field is ;ero at the center field is ;ero at the center <<

/

2 )

32 (

32 ( 32 (

32 (

ConcepTest 16./bConcepTest 16./b Superposition --Superposition --



5% @ 0

ollow3up4ollow3up4 $hat if the upper two charges were =2 (1$hat if the upper two charges were =2 (1

$hat if the right3hand charges were =2 (1 $hat if the right3hand charges were =2 (1

C T t 16 /C T t 16 / S iti ---S iti ---



$hat is the direction of

the electric field at the

position of the 0 1

/2

)

=#

3# =#

5

ConcepTest 16./c ConcepTest 16./c Superposition ---Superposition ---

C T t 16 /C T t 16 / S iti ---S iti ---



The two =# charges give a resultant field

that is down and to the rightdown and to the right The ># charge

has an field up and to the leftup and to the left. but s"aller s"aller in "agnitude Therefore. the total electrictotal electric

field is down and to the rightfield is down and to the right

$hat is the direction of

the electric field at the

position of the 0 1

/2

)

=#

3# =#

5

ConcepTest 16./c ConcepTest 16./c Superposition ---Superposition ---

ollow3up4ollow3up4 $hat if all three charges reversed their signs1 $hat if all three charges reversed their signs1

C T t 16 1(C T t 16 1( i d th (hi d th (h



)% charges are eEual and positive

2% charges are eEual and negative

/% charges are eEual and opposite

% charges are eEual. but sign is

undeter"ined

5% charges cannot be eEual

?2?)

y

Two charges are fi&ed alongTwo charges are fi&ed along

thethe 3a&is They produce an3a&is They produce an

electric fieldelectric field directed alongdirected along

the negativethe negative y y 3a&is at the3a&is at the

indicated point $hich ofindicated point $hich of

the following is true1the following is true1

ConcepTest 16.1( ConcepTest 16.1( ind the (hargesind the (harges

C T t 16 1(C T t 16 1( i d th (hi d th (h



The way to get the resultant P-67 vector

is to use the +,,6 and F9U, vectors

These vectors correspond toeEualeEual

chargescharges #because the lengths are eEual%

that are both negativeboth negative #because their

directions are toward the charges% ?2?)

y

Two charges are fi&ed alongTwo charges are fi&ed along

thethe 3a&is They produce an3a&is They produce an

electric fieldelectric field directed alongdirected along

the negativethe negative y y 3a&is at the3a&is at the

indicated point $hich ofindicated point $hich of

the following is true1the following is true1

)% charges are eEual and positive

2% charges are eEual and negative

/% charges are eEual and opposite

% charges are eEual. but sign is

undeter"ined

5% charges cannot be eEual

ConcepTest 16.1( ConcepTest 16.1( ind the (hargesind the (harges

ollow3up4ollow3up4 How would you get theHow would you get the field to point toward the right1field to point toward the right1

C T t 16 11ConcepTest 16 11 U if ,l t i i ldUnifor" ,lectric ield



?

-n a unifor" electric field in e"pty-n a unifor" electric field in e"pty

space. a ( charge is placed and itspace. a ( charge is placed and it

feels an electrical force of )2 6 -ffeels an electrical force of )2 6 -f

this charge is re"oved and a * (this charge is re"oved and a * (

charge is placed at that pointcharge is placed at that point

instead. what force will it feel1instead. what force will it feel1

)% )2 6

2% C 6

/% 2 6

% no force

5% )C 6

ConcepTest 16.11ConcepTest 16.11 Unifor" ,lectric ieldUnifor" ,lectric ield

C T t 16 11ConcepTest 16 11 U if ,l t i i ldUnifor" ,lectric ield



Since the ( charge feels a force. there "ust

be an electric field present. with "agnitude4

+ F % + 12 % & C + 3 %C + F % + 12 % & C + 3 %C

:nce the ( charge is replaced with a * (

charge. this new charge will feel a force of4

F + + "6 C$"3 %C$ + 1 F + + "6 C$"3 %C$ + 1

?

)% )2 6

2% C 6

/% 2 6

% no force

5% )C 6

ConcepTest 16.11ConcepTest 16.11 Unifor" ,lectric ieldUnifor" ,lectric ield

ollow3up4ollow3up4 $hat if the charge is placed at a$hat if the charge is placed at a di))erent positiondi))erent position in the field1in the field1

-n a unifor" electric field in e"pty-n a unifor" electric field in e"pty

space. a ( charge is placed and itspace. a ( charge is placed and it

feels an electrical force of )2 6 -ffeels an electrical force of )2 6 -f

this charge is re"oved and a * (this charge is re"oved and a * (

charge is placed at that pointcharge is placed at that point

instead. what force will it feel1instead. what force will it feel1

ConcepTest 16 12aConcepTest 16 12a ,lectric ield 9ines -,lectric ield 9ines -



ConcepTest 16.12aConcepTest 16.12a ,lectric ield 9ines -,lectric ield 9ines -

$hat are the signs of the

charges whose electric

fields are shown at right1

)%

2%

/%

%

5% no way to tell

ConcepTest 16 12aConcepTest 16 12a ,lectric ield 9ines -,lectric ield 9ines -



ConcepTest 16.12aConcepTest 16.12a ,lectric ield 9ines -,lectric ield 9ines -

$hat are the signs of the

charges whose electric

fields are shown at right1

)%

2%

/%

%

5% no way to tell

,lectric field lines

originate onoriginate on

positive chargespositive charges and ter"inateter"inate

on negative chargeson negative charges

ConcepTest 16 12bConcepTest 16 12b ,lectric ield 9ines --,lectric ield 9ines --



ConcepTest 16.12bConcepTest 16.12b ,lectric ield 9ines --,lectric ield 9ines --

$hich of the charges hasthe greater "agnitude1

)%

2%

/% Foth the sa"e

ConcepTest 16 12bConcepTest 16 12b ,lectric ield 9ines --,lectric ield 9ines --



ConcepTest 16.12bConcepTest 16.12b ,lectric ield 9ines --,lectric ield 9ines --

$hich of the charges hasthe greater "agnitude1

)%

2%

/% Foth the sa"e

The field lines are denser arounddenser around

the red chargethe red charge. so the

red onered one

has the greater "agnitudehas the greater "agnitude

ollow3up4ollow3up4 $hat is the redBgreen ratio$hat is the redBgreen ratio

electrostatics ct solution

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