university physics: waves and electricity ch21. coulomb’s law lecture 6 dr.-ing. erwin sitompul

University Physics: Waves and Electricity

Ch21. Coulomb’s LawLecture 6

Dr.-Ing. Erwin Sitompulhttp://zitompul.wordpress.com

6/2Erwin Sitompul University Physics: Wave and Electricity

Homework 5: Ambulance Siren

An ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyclist pedaling a bike at 8 m/s. After being passed, the cyclist hears a frequency of 1590 Hz.

(a) How fast is the ambulance moving?(b) What frequency did the cyclist hear before being overtaken

by the ambulance?


Solution of Homework 5: Ambulance Siren

(a)1590 Hzf 8 m s , toward Dv S

D

S

v vf f

v v

1600 Hzf

?, away from Sv D

343 81590 1600

343 Sv

1590(343 ) 1600(343 8)Sv

10.21 m sSv 545370 1590 561600Sv

(b)

?f 8 m s , away from Dv S

1600 Hzf

10.21 m s , toward Sv D

D

S

v vf f

v v

343 81600

343 10.21

1610.63 Hz


Electric Charge

Static cling, an electrical phenomenon that accompanies dry weather, causes the pieces of paper to stick to one another. This is an example that reveals the existence of electric charge.

In fact, every object contains a vast amount of electric charge.

Electric charge is an intrinsic characteristic of the fundamental particles making up those objects.

The vast amount of charge in an everyday object is usually hidden because the object contains equal amounts of the two kinds of charge: positive charge and negative charge.

With such a balance of charge, the object is said to be electrically neutral (contains no net charge).

If the two types of charge are not in balance, we say that an object is charged, it has a net charge.


Electric Charge

Charged objects interact by exerting forces on one another.

Charges with the same electrical sign repel each other, while charge with opposite electrical signs attract each other.

This rule will be described quantitatively as Coulomb’s law of electrostatic force between charges. (The term electrostatic is used to emphasize that the charges are stationary relative to each other.)


Coulomb’s Law

If two charged particles are brought near each other, they each exert a force on the other.

If the particles have the same sign of charge, they repel each other. The force on each particle is directed away from the other particle.

If the particles have opposite signs of charge, they attract each other. The force on each particle is directed toward the other particle.


Coulomb’s Law

This force of repulsion or attraction due to the charge properties of objects is called an electrostatic force.

The equation giving the force for charged particles is called Coulomb’s law, named after Charles-Augustin de Coulomb, who did the experiments in 1785.

If particle 1 has charge q1 and particle 2 has charge q2, the force on particle 2 is:

1 22 122

12

rq q

F kr

The term is a unit vector to the direction from position of q1 to position of q2. The term k is a constant.

12r

9 2 2

0

18.99 10 N m C

4k

12 2 20 8.854 10 C (N m )


Coulomb’s Law

ε0 is a constant denoted as permittivity in vacuum, a measure of how the vacuum medium is affected by an electric field.

As can be deducted from the constants, the SI unit of charge is the coulomb (C).

x

yq1

q2

r12

→

r1

→

r2

→

1 22 122

12

ˆq q

F k rr

12 2 1r r r

1212

12

ˆr

rr

2 1

2 1

r r

r r

F2

→

+

+


Some Examples on Vectors

Example: If , find and . 12ˆ ˆ4i 2 jr

12r

12r2 2

12 (4) (2)r

20 4.472

1212

12

ˆr

rr

ˆ ˆ4i 2 j

4.472

ˆ ˆ0.894i 0.447 j

Example: If and , find and . 1ˆ ˆ2i 3jr

12r

21r2ˆ ˆ4i 2 jr

12 2 1r r r ˆ ˆ ˆ ˆ(4i 2 j) (2i 3j) ˆ ˆ2i 5j

21 1 2r r r ˆ ˆ ˆ ˆ(2i 3j) (4i 2 j) ˆ ˆ2i 5j

12 21r r

12 21r r Both vectors are of

opposite direction, but have the same magnitude


Coulomb’s Law

If we have n charged particles, they interact independently in pairs, and the force on any one of them, is given by the vector sum.

Let us say, we have n particles, then the force on particle 1 is given by:

1,net 12 13 14 1nF F F F F

x

yq1

q2

+

–q3

F21

→

F23

→

F2,net

→

+


Example 1: Coulomb’s Law

1 212 212

21

ˆq q

F k rr

1 0r

2ˆ0.02i mr

21 1 2r r r ˆ0.02i

21 0.02r

2121

21

ˆr

rr

i

The figure below shows two positively charged particles fixed in place on an x axis. The charges are q1 = 1.610–19 C and q2 = 3.210–19 C. The q1 is located on the origin, while the separation is R = 0.02 m.What are the magnitude and direction of the electrostatic force F12 on particle 1 from particle 2?

19 199

2

(1.6 10 )(3.2 10 ) ˆ8.99 10 ( i)(0.02)

24 ˆ1.151 10 i N

→



Now, particle 3 lies on the x axis between particles 1 and 2. Particle 3 has charge q3 = –3.210–19 C and is at a distance 3/4R from particle 1.What is the net electrostatic force F1,net on particle 1 due to particles 2 and 3?

→

1 0r

3ˆ0.015i mr

31 1 3r r r ˆ0.015i

31 0.015r

3131

31

ˆr

rr

i

1 313 312

31

ˆq q

F k rr

19 19

92

(1.6 10 )( 3.2 10 ) ˆ8.99 10 ( i)(0.015)

24 ˆ2.046 10 i N

1,net 12 13F F F

24 24ˆ ˆ1.151 10 i 2.046 10 i 25 ˆ8.95 10 i N



Particle 3 from previous example is now replaced by particle 4. Particle 4 has charge q4 = –3.210–19 C, is at a distance 3/4R from particle 1, and lies on a line that makes an angle θ = 60° with the x axis.What is the net electrostatic force F1,net on particle 1 due to particles 2 and 4?

→

1 0r

4ˆ(0.015)cos60 i

ˆ (0.015)sin 60 j r

41 1 4r r r

ˆ ˆ0.0075i 0.013j

2 241 ( 0.0075) ( 0.013)r

4141

41

ˆr

rr

ˆ ˆ0.0075i 0.013j

3

40.015, equals R

ˆ ˆ0.0075i 0.013j

0.015

ˆ ˆ0.5i 0.867 j



1 414 412

41

ˆq q

F k rr

19 19

92

(1.6 10 )( 3.2 10 ) ˆ ˆ8.99 10 ( 0.5i 0.867 j)(0.015)

24 24ˆ ˆ1.023 10 i 1.774 10 j N

1,net 12 14F F F

24

24 24

ˆ1.151 10 iˆ ˆ (1.023 10 i 1.774 10 j)

24ˆ ˆ( 0.128 i 1.774 j) 10 N


Checkpoint

The figure below shows three arrangements of one electron (e) and two protons (p).(a) Rank the arrangements according to the magnitude of the

net electrostatic force on the electron due to the protons, largest first

(b) In situation c, is the angle between the net force on the electron and the line labeled d less than or more than 45 °?

191.602 10 Cp 191.602 10 Ce

a, c, b

Less than 45°



Two particles are fixed in place: a particle of charge q1 = +8q at the origin and a particle of charge q2 = –2q at x = L.At what point can a particle of charge q3 = +4q be placed so that it is in equilibrium (the net force on q3 is zero)?

: impossible to place q3 on the left of q1 or in the middle between q1 and q2

: the only possibility is to place q3 to the right-hand side of q2

F31

→

F32

→

F32

→

F31

→

F32

→

F31

→



3,net 31 32 0F F F

F32

→

F31

→

1 3 2 313 232 2

13 23

ˆ ˆ 0q q q qk r k rr r

1 3 2 32 2

13 23

ˆ ˆi i 0q q q qk kr r

1 22 2

13 23

0q q

r r

2 2

8 20

( )

q q

L x x

2 2

8 2

( )L x x

2 28 2( )x L x 2 2 28 2( 2 )x L xL x

2 26 4 2 0x L x L

ca b

2

1,2

4

2

b b acx

a

11 3x L

2x L • q3 to the right of q2

• q3 between q1 and q2

L x

Charge q3 must be placed on the x axis, at distance L to the right of q3, or, at point (2L,0)