Lesson 27 Coulombs Law

8/10/2019 Lesson 27 Coulombs Law

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Physics 30 Lesson 27 Coulomb’s Law

I Historical development of Coulomb’s Law

In 1775, Ben Franklin noted that a small neutral cork hanging near the surface of anelectrically charged metal can was strongly attracted to the outside surface of the metalcan.

When the same cork was lowered inside the can, the cork was not attracted to the

surface of the can. Franklin was surprised to discover no attraction within the can utstrong attraction outside the can.

!oseph "riestly was a house guest of Ben Franklin in 1775. "riestly had een studyingscience at #amridge, ut he fled from $ngland ecause of religious persecution.Franklin asked "riestly to repeat his e%periment. "riestly otained the same results asFranklin, ut the e%periment triggered memories of &ewton's discussion of gravitywithin a hollow planet. &ewton had e%amined the possiility of gravity inside a hollowplanet in his ook Principia Mathematica ("rinciples of )athematics*. &ewton came tothe conclusion that any point inside the hollow planet would e su+ect to forces fromthe surface ut the forces would all cancel out leaving the appearance of nogravitational field.

"riestly reasoned that the appearance of no net electrical forces inside the metal canmight e very similar to gravity within the hollow planet. "riestly suggested that thise%periment showed that electrical forces were very similar to gravitational forces.

7 - 1



#harles #oulom 17/0 - 1023 was veryintrigued y "riestly's intuitive connectionetween electrostatic forces and gravitationalforces. 4e immediately egan to test therelationship using a torsion balance. 4emeasured the force of electrostatic repulsionusing the torsion alance as diagrammed to theright.

If 3 and a3 have the same charge then they will repel each other causing the rod towhich a3 is attached to twist away from 3. he force necessary to twist the wireattached to the rod holding a3 could e determined y first finding the relationshipetween the angle of torsion and the repulsive force. hus, #oulom had a way tomeasure the force of repulsion.

#oulom then egan to test the effect of increasing the charge on oth a3 and 3 andhe found that the repulsive force increased. $ventually he found that the electrostaticforce was directly proportional to the product of the charge on each o+ect.

F 6 6e ∝

1 , 61 charge on a36 charge on 3

#oulom then tested to see the effect of increasing the distance etween a3 and 3and found that the force decreased y the s6uare of the distance etween the twoo+ects.

Fr e ∝

1,

r distance etween charges center to center3

When #oulom comined the two relationships together he found that the electrostatic

force varied directly as the product of the two charges and inversely as the s6uare ofthe distance etween the two charged o+ects.

F6 6

r e ∝

1 ,

,

fter repeated measurements where the charges and distances were known, he was

ale to replace the proportionality sign ∝ with k3 which is known as #oulom's

constant and has a value of 8

7 -



k 9 0.:: % 1: & m

#

7 - /



he final result is known as #oulom's ;aw of electrostatic attraction.

F k6 6

r e =

1 ,

,

he relationship is very similar to &ewton's <niversal =ravitation ;aw and theconnection predicted y "riestly's intuitive leap was confirmed.

II lectrostatics problems

Example 1

What is the electrostatic force of attraction etween a 0. % 1 -2 # charge and a2. % 1-5 # separated y .5 m>

Fe 9 k 616 9 0.:: % 1: & m ?# 0. % 1-2 #32. % 1-5 #3 9 ! "72# $r .5 m3

&ote8

⇒ he minus sign for a final answer indicates an attractive force.

⇒ positive answer would indicate a repulsive force.

⇒ he si@e of electrostatic forces is very large when compared to gravitational forces.

Example 2

fi%ed charge of 5. % 1-A # acts upon a 5. g mass which has a charge of 7. % 1 -A #. If the charges are .5 m away from one another, what is the acceleratione%perienced y the 5. g mass>

Fe 9 k 616 9 0.:: % 1: & m ?# 5. % 1-A #37. % 1-A #3 9 1502 &r .5 m3

a 9 Fnet 9 1502 & 9 2%&2 ' "0# m(s2 away from the first char)em .5 kg

Example 3

If the attractive force etween two e6ually charged particles is :. % 1 2 & and thedistance etween them is .5 cm, what is the charge on each particle>

61 will e e6ual to 6 61 9 63 ut opposite in sign attraction3Fe 9 k 616 9 k 6161 9 k 61

r r r

6 F r

k

% & m

% &m #e

1

, 2 ,

: , ,

: 1 5

0 : : 1 = =

. . 3

. ? 9 1.50 % 1-A # 61 9 !"%&* ' "0+, C

6 9 +"%&* ' "0+, C

Example 47 - A



When two charged particles are set a certain distance apart, a repulsive force of 0. &e%ists. What is the force of repulsion etween the two particles if the distance etweenthem is douled and one of the charges is tripled in si@e>

In this solution, write the e6uation and then whatever is done to one side is done to the other side as well.

,,1

$r

66kF =

3,%r

3/%66k,

3/%&.0,,

,1

, =

F$C 9 #%0 $

Example 5

A µ# charge and a 12 µ# charge are set :. m apart. n unknown positive

charge is placed on a line +oining the first two charges and it is allowed to move until it

comes to rest etween the two charges. t what distance measured from the 12 µ#

charge will the unknown charge come to rest>

he charge will come to rest where the forces from and B are e6ual to each other.

F # 9 FB#

k 6 6# 9 k 6B6#

:.-%3 %

6 9 6B

:.-%3 %

6 % 9 6B:.-%3

6 % 9 :.-%3

6B

A µ# % 9 :.-%3

12 µ#

.5 % 9 :.-%3 take s6uare root of oth sides3

.5 % 9 :. - %1.5 % 9 :.% 9 #%0 m

7 - 5

A µ#

B

12 µ#

#3 charge

%:. - %

:. m



Example 6

From the diagram elow determine the net electrostatic force on #.

we need to calculate the #distance and angle

# 9 .1 .7531?

# 9 .15 m

tan θ 9 .1 ? .75

θ 9 5/.1o

here are two forces acting on charge #8 FB# and F #. We calculate their magnitudes.

FB# 9 k 6B6# 9 0.:: % 1: & m ?# /. % 1-2 #3A. % 1-2 #3 9 1:.10 &r B#

.75 m3

F # 9 k 6 6# 9 0.:: % 1: & m ?# . % 1-2 #3A. % 1-2 #3 9 A.2 &r #

.15 m3

he free ody diagram is8

s we learned in physics , we canadd these vectors together y reakingthe A.2 & force into its north and westcomponents.

dding all of the components together8

east-west3 9 /.20 westnorth-south3 9 .72 north 1:.10 south 9 12.A south

F&$ 9 12.A /.2031? 9 12.0 &

tan θ 9 /.20 ? 12.A

θ 9 1.2o W of D

F &$ 9 "#%* $ at "2%#o - of .

7 - 2

• •

•

B

/. µ#

-. µ# .1 m

.75 m

#

A. µ#

•

θ

A.2 &

1:.10 &

5/.1o

A.2F #&3 9 A.2 cos5/.1F #&3 9 .72 north

F #W3 9 A.2 sin5/.1

F #&3 9 /.20 west

12.A &

/.20 &

θ

F&$



III Practice problems

1. #alculate the electric force etween two point charges of A. µ# and /. µ#

when they are . cm apart. 7 &3

. wo point charged o+ects produce an electric force of .2 & on each other.What is the electric force if the distance etween them increases three times andone of the charges is douled> .1/0 &3

/. wo point charges produce a repulsive force of ./A & when placed .1 mapart. What is the charge on each point charge if the magnitude of the larger

charge is three times the magnitude of the smaller charge> .11 µ#, .//2 µ#3

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A. wo small spheres, each with a mass of . % 1-5 kg are placed ./5 m apart.

Ene sphere has a charge of -. µ# and is fi%ed in position. he other sphere

has a charge of -/. µ# and is free to move. What is the initial acceleration of

the second sphere> oes the gravitational force have any effect on theacceleration of the sphere> . % 1A m?s3

Lesson * Hand+in assi)nment

Part / lectrostatics revisited

1. 4ow could a neutral insulated metal conductor e given a negative charge using8 . a negatively charged rod>B. a positively charged rod>

<se diagrams to support your answer.

. Why does ruing a conductor not produce a static charge whereas ruing an

insulator can produce a static charge>

/. What is the net charge on a metal sphere having an e%cess of 1. % 11 electrons> -1.2 % 1-: #3

A. What is the net charge on a metal sphere having a deficit of 1. % 11 electrons>1.2 % 1-7 #3

5. If a negatively charged rod is rought near the kno of a positively chargedelectroscope, what will happen to the separation etween the leaves of theelectroscope> $%plain.

2. positively charged rod is rought near an electroscope that is already charged.If the leaves spread further apart, what kind of charge does the electroscopehave> $%plain.

7. =iven a solid metal sphere and a hollow metal sphere, each with the same radius,which will hold the greater charge> !ustify your answer.

0. metal sphere with an e%cess of 7.75 % 11: protons is touched to anotheridentical neutral metal sphere. What is the final charge on each sphere> 2. #3

7 - 0



:. <sing a diagram, show how a neutral electroscope could e charged y apositively charged rod using induction. What is the final charge on theelectroscope>

Part 1 Coulomb’s Law problems

1. Find the force of electrostatics attraction etween a 1 µ# charge and a

-5. µ# charge located 5. cm apart. -10. &3

. If the force of attraction etween two charges is /1 &, what will e the force ifone of the charges is made four times larger and the distance is reduced to half of its original value> A.:2 k&3

/. What charge G placed A. cm from a charge of 0 n# will produce a repulsiveforce of .15 &> /./ % 1-0 #3

A. wo small metallic spheres have the same mass and volume. Ene of the spheres

has a charge of A. µ# and the other a charge of -1. µ#. If the two spheres

are rought into rief contact with each other and are then separated to adistance of . m, what is the electric force etween them> .52 &3

5. escrie ways to give a neutral electroscope a positive charge, using only apiece of silk and a glass rod. #ould the same materials e used to give it anegative charge> If so, how>

2. #ompare &ewton's ;aw of <niversal =ravitation with #ouloms ;aw, pointing outthe similarities and differences.

7. wo small, oppositely charged spheres have a force of electric attraction etween

them of 1.2 % 1-

&. What does this force ecome if each sphere is touched withit's identical, neutral mate, and then replaced twice as far apart as efore> hemates are taken far away. 1. % 1 -/ &3

0. Ene model of the structure if the hydrogen atom consists of a stationary protonwith an electron moving in a circular path around it, of radius 5./ % 1 -11 m.

a3 What is the electrostatic force etween the electron and the proton> 0. %1-0 &3

3 What is the gravitational force etween them> /.2 % 1-A7 &3c3 Which force is mainly responsile for the electron's centripetal motion>d3 #alculate the velocity and period of the electron's orit around the proton.

. % 12 m?s, 1.5 % 1-12 s3

7 - :



H:. wo small, identical, charged spheres attract one another with a force of 0. % 1-5

&, when they are / cm apart. hey are touched together, and are again placed/ cm apart, ut they now e%ert a force of repulsion of 1. % 1 -5 & on each other.

a3 What is the charge on each sphere after they are touched> 1. % 1 -0 #,same signs3

3 What was the charge on each efore they were touched> A. % 1-0 # and. % 1-0 #, opposite signs3

1. ssume that a single, isolated electron is fi%ed at ground level. 4ow far aove it,vertically, would another electron have to e, so that its mass would e supportedy the force of electrostatic repulsion etween them> 5.1 m3

11. wo small charges, A. % 1-5 # and -1.0 % 1-5 #, are placed A cm apart. Whatis the force on a third small charge, of magnitude -.5 % 1 -2 #, if it is placed onthe line +oining the other two, and

a3 1 cm to the outside of them, on the side of the negative one> 1 & awayfrom negative charge3

3 1 cm to the outside of them, on the side of the positive one> 5: & towardpositive charge3

H1. From the diagram elow, point charges and are oth 5 µ# and B and # are

oth -5 µ#. What is the net force on > 011 & A.5o $ of D3

1/. wo positive charges A. cm apart repel each other with a force of .: &. Ene of the charges is known to e four times larger than the other charges. Find themagnitude of the larger charge. 0. % 1 -7 #3

1A. In the diagram elow, has a charge of ./ µ#, B has a charge of -. µ# and

# has a charge of -. µ#. What is the net force on > .:/ & JDK3

7 - 1

B

#

5. cm

1 cm

•

•

•

B

1 cm 1 cm

#1 cm



15. hree charges are placed as shown in the diagram elow. What is the net force

on the A. µ# charge> .5 & 5/o D of $3

12. small negatively charged Dtyrofoam all lying on a tale is pulled upward fromthe tale at a constant speed y the electrostatic force etween it and anotherDtyrofoam all held . cm aove it. ssuming the alls have the samemagnitude of charge and the same mass .1 g3, what is the smallest possilecharge on the all on the tale> 2.2 % 1 -: #3

H17. wo positive charges 5. µ#3 and B µ#3 are 1. cm apart. third

charge # A. µ#3 is placed in the line etween and B and it is free to move

along the line. t what point, measured from B, will charge # come to rest> 0 cm3

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• •

•

A.

µ#

/.

µ#

.2 m

.2 m

-A.

µ#

Lesson 27 Coulombs Law

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