CHAPTER III
ELECTROSTATIC
Subject:
1. Electrostatics interaction and coulomb’s law 2. Electric field
3. Gauss’s law
4. Electric potential and electric potential energy 5. Capacitors
1. Electrostatics interaction and coulomb
the statement of coulomb’s law “ the force between two charged object is directly proportional to
the cross product of their charges and inversely proportional to the distance between them”
we can be expressed that statement by equation below:
where
If the interaction of electric charges occurs in air (vacuum)
o= 8.85 x 10-12 C2N-2m-2But if interaction of electric charge occurs in anther material
ochange with
wherey
permitivit
vacuu
air
y
permitivut
material
vacuum
the
to
relative
y
permitivit
material
r
0
2 2 1r
q
q
k
F
F= Coulomb force (N) q1= charge of object 1 (C) q2= charge of object 2 (C) k= constant (9 x 109 ) mN2C-2r = distance between q1 with q2 (m)
o
k
4
1
o r
B C A r r r Exercise
1. Two charges each of 20 µC and 24 µC are separated 12 cm, calculate the repulsion force on the charge if: a. both charges are place in air
b. both charges are place in a substance with
r= 5
2. at corner points of an equilateral triangles ABC are placed the charges each of qA = +20 µC, qB = -40 µC and qC
= -40 µC, as shown in the following figure
If r = 8 cm, determine the force that exerts upon the charge qA
3. At the corner points of the square ABCD are placed the charges consecutively +q, -q, -q and –q. the side length of the square is s and the charge +q experiences the force of , determine:
a. medium where the charges exist b. the value of n
c. force upon the charge of +q if q = 30 µC and s = 15 cm
4. at the corners of an equilateral triangle that is 12 cm in side length are placed 3 charges, these are q1= 14
µC, q2=3.4 µC and q3= -20
3
µC.Determine the force exerts upon the charge q
T m=20 kg q=+ 0.5 µC 15 cm q'=- 1 µC -9 µC +5 µC -4 µC
5. an object that has mass of 20 grams and charge +0.5 µC. It is suspended on the string as in the following figure
If the string mass is neglected calculate the string tensional force (T) 6. two changes each of 20 µC and -60 µC are separated 18 cm. if the chargers are placed on the substance that has the relative permittivity of 8, calculate the coulomb’s force on the charges
7. A particle charged + 5 µC is placed on a connector line and between two charged particles of -9 µC and -4 µC that separated 0.5 m. determine the position of particle +5 µC so hat is not undergo the coulomb’ s force from the two other charges
8. ada empat buah muatan A, B, C, D. A mmenarik B. A enolak C, dan C menarik D. Bila C bermuatan negatif tentukan jeis muatan-muatan lainnya
9. Hitunglah nilai perbandingan antara gaya coulomb dengan gaya gravitasi yang dikerjakan oleh sebuah proton terhadap proton lainnya
10. dua keping uang logam masing-masing diberi muatan sama, terpisah sejauh 15 cm. Gaya tolak menolak antara
kedua uang logam 6,4 x 10-6 N. Hitunglah muatan masing-masing uang logam jika keduanya berada:
a. di udara
b. di dala air yang permitifitas relatifnya 80
11. muatan titik A, 250 µC, diletakkan pada garis hubung antara muatan titik B, 50 µC, dan muatan titik C, -300 µC. Muatan titik A diletakkan 5 cm dari B dan 10 cm dari C. Tentukan besar dn arah gaya yang bekerja pada muatan titik A
12. bola kecil A bermuatan +135 µC dan bola kecil B bermuatan -60 µC terpisah sejauh 10 cm. Bola kecil C yang bermuatan diletakkan pada garis hubung antara A dan B sehingga resultan yang bekerja pada C sama dengan nol. Dimana letak C diukur dari A?
13. Muatan q1= -2 x 10-6 Cdan q2= 3 x 10-6 C
terletak masing-asing pada titik A (8,0) dan B (0,10) dalam suatu sistim koordinat kartesius. Semua satuan panjang dala sm. Hitungllah besar dan arah gaya pada muatan q3=-10-6C yang
diletakan pada titik asal koordinat 14. Dua bola kecil digantung seperti
gambar dibawah. Tiap bola memiliki massa 5 gram, dan bermuatan q. Panjang tali 30 cm. Kedua bola mencapai keseimbangan ketika θ=900.
2. Electric Field (E)
The electric field strength of a charge (q) when an experiment charge (q) is placed at distance of r from that charge can be determined by the equation follows
Electric Flux
Is defined as the number of electric field lines that pierce a closed surface, that mathematically expressed by the following equation :
Gauss’s Law
“ the number the electric field lines that penetrate a closed surface is proportional with the amount of electric charge covered by the closed surface, can be expressed by the equation as fallow
The Application of Gauss’s Law
1. Electric field strength between parallel charged plates
2. Electric field strength by the charged conductor ball
2
r
kq
E
E = electric field strength (N/C)
cos
EA
electric flux (weber)
θ = the angle between E with the
normal line of the plane
0
cos
q
EA
0
E
charge density (C/m
2)
2r
kq
E
-2q
+18q 7 cm
Exercise
1. what is the electric field strength at 0.5 mm from a charge of +2µC (7.2 x 1010 N/C)
2. at corner points of B and D of a square ABCD are placed a charged particle of +q. determine the charge of particle that must be located at point C so that the electric field at A is zero
3. Two point charges consecutively +8 µC and +12 µC are separated 15 cm from each other. Determine the location of a poin from +8 µC charge that its electric field strange is equal to zero
4. To charge each of +2.5 µC and -7 µC are located 10 cm from each other. Determine a) the electric field strength in the
middle
b) the force exert upon the charge of +8 x 1017C in the middle
5. Two particle A and B are consecutively charge +20 µC and 45 µC and separated 15 cm. if C is placed between A and B. so that Ec=0. determine the location of C from A
6. Pada gambar dibawah ini dimanakah letak titik yang kuat medannya nol ?
7. A spherical conductor has radius 15 cm and charged 30 µC with uniform distribution of charges in the surface. Determine:
a) the charge density in the ball surface b) the electric field strength at 5 cm
c) the electric field strength in the surface
d) the electric field strength at 18 cm from the canter of the ball
8. Explain the definition of the following terms
a) electric flux b) Gaussian surface c) Charge density
9. Explain why the value of E inside the conductor ball is ziro
10. A conductor ball has radius of 10 cm. if its charge is 2C determine :
a) E at 5 cm in canter of the ball b) E at 10 cm in canter of the ball c) E at 15 cm in canter of the ball 11. Two opposite parallel plates charged Q = 3
µC and the area is 6 cm x 1.5 cm. determine
a) Charge density
b) Electric field strength between the plates
12. hitunglah jumlah garis medan yang menembus bidang persegi (sisi = 25 cm) bila vector medan listrik homogen sebesar 120 N/C
13. Sebuah konduktor keping sejajar yang tiap kepingnya berbentuk persegi dengan panjang sisi 30 cm. Diberi muatan 7.08 µC yang berlawanan jenis, hitung:
a) Rapat muatan listrik tiap keping b) Besar kuat medan listrik dalam ruang
diantara kedua keping
14. Sebuah konduktor bola berongga yang jari-jarinya 4 cm diberi muatan +0,2 µC. Titik-titik A, B dan C berturut-turut jaraknya 2 cm, 4 cm dan 6 cm dari pusat bola. Hitung kuat medan listrik dititik A, B dan C
3. Electric Potential
Electric potential is defined as the charge of potential energy per unit charge when an experiment charged is move between to point.
Can be determined by the following equation:
Electric potential energy
Is the multiply between electric potential with experiment charge
Work
If an experiment charge (q0)in the electric field of a source charge (q) is moved from position A to
position B, then the value of work required is equal to the change of potential energy (ΔEp)
ΔEp = W
So that
Equipotential Planes
Electric Potential by The Charged Conductor Ball
The electric potential inside the charged conductor ball R = Radius of te ball
r = Point distance to the center of the ball
While the electric potential outside the ball
Electric Potential Between Two Charged Parallel Plates
Mechanical Energy Conservation Law
r
kq
V
V
q
E
p
r
k
E
p 0
)
1
1
(
0 A Br
r
q
kq
W
W
q
0
V
0
W
R
kQ
V
r
kQ
V
d
E
V
.
V
.
d
V
.
d
0
2 2 2 2 1 12
1
2
1
mv
qV
mv
qV
EXERCISE 1. Tentukan perubahan energi listtrik ketika
sebuah elektron dalam atom hidrogen (muatan –e = -1,60 x 10-19 C) bergerak dari
suatu keadaan tereksitasi pada r = 2,00 x 10-10 m ke keadaa energi terendahnya pada r = 5 x 10-11 m
2. Sebuah bola kecil dimuati +2,00 x 10-6 C
a. hitung beda potensial antara
kedudukan awal yang jauhnya 0,900 m dari muatan dan kedudukan akhir yang jauhnya 0,600 m dari muatan
b. berapa perubahan energi potensial yang terjadi jika bola lain bermuatan -5,00 x 10-8 C digerakkan diantara kedua kedudukan ini ?
c. apakah perubahan energi potensial pada (b) bertambah atau berkurang ? 3. Dua buah muatan q1= +2,00 x 10-6C dan
q2 = -5,00 x 10-6 C terpisah sejauh
0,400 m. Tentukan potensial pada suatu titik ditengah-tengah antara kedua muatan tersebut
4. Pada keempat sudut sebuah persegi (sisi = 30 cm) diletakkan muatan-muata titik yang sama -6,0 µC. Hitung potensial listrik dipusat persegi itu
5. Proton yang bergerak dari A ke B memperoleh kecepatan 2 x 105 m/s. Jika
diantara dua keping vakum, d = 1 cm, dan massa proton = 1,6 x 10-27kg, muatan
proton 1,6 x 10-19C, tentukan beda potensial keping sejajar ini
6. Beda potensial 4 kV diberikan antara ujung-ujung sebuah konduktor kepig sejajar yang terpisah sejauh 10 cm. Tentukan:
a. kuat edan listrik dalam ruang antar keping
b. beda potensial antara titik yang berjarak 4 cm dari keping positif terhadap keping negatifnya 7. Muatan 2,75 x 10-8C didistribusikan
merata pada sebuah konduktor bola berongga yang diameternya 150 mm a. berapa potensial listrik dikulit bola ? b. berapa potensial listrik pada tepat
yang berjarak 50 mm dari pusat bola? c. Hitung energi potensial sebuah muatan
1,25 x 10-5 C yang diletakkan 250 mm dari pusat bola
8. Sebuah elektron (muatan –e ) diletakkan pada setiap dari kedelapan titik sudut dari sebuah kubus degan panjang rusuk a, dan sebuah partikel (muatan +2e) pada pusat kubus tersebut, hitunglah energi potensial sistim
9. the electric potential at a point that has distance of r from charge Q is 300 volt. The electric field strength at that point is 800 N/C. determine the amount of charge Q ( 1.25 x 10-8 C )
10. A conductor ball has diameter of 20 cm and is charged 100 µC . determine : a. electric potential at 5 cm from the
center of the ball (9 x 106 volt)
b. electric potential at 10 cm from the surface of the ball (45 x 1055 volt)
11. what is the work required to move the positive charge of 10 C from one point (V1=10 volt) to another (V2=60 volt)?
12. The potential difference between two parallel plates with equal and opposite charges is 400 volt within an empty cylinder. If the electrons from the negative plate are accelerated toward positive plate with v0=0, then determine
the speed of electrons when strike the positive plate (me = 9.11 x 10-31 kg and e =
-1.6 x 10-19 C)
13. The electric potential at a point that has distance of 2 cm from a point charge is 0.4 volt. Determine the electric potential at 8 cm from the charge
14. In the corner points a square ABCD locate the charges consecutively +42 µC. -42 µC, +42 µC and -42 µC. Determine the electric potential at :
a. the center of the square, if the side length is 12 cm
b. in the middle side between A and B 15. A charged conductor ball (Q = 200 µC) has
radius of 15 cm. determine the work required to move an electron (e = -1.6 x 10-19 C) from the surface of the ball so that it is not influenced by the ball’s charge
D
A B
16. The right triangle ABC has the length AB = 4 cm and AC = 3 cm and at every corner locates the electric charges of qA = +10-10
C, qB = -10-10C and qC = -10-10C, as shown
the figure below, calculate the work required to move qC to D
17. An electron is shot by speed of 5000 m/s in parallel direction with electric field (E = 2000 V/m). what is the greatest distance reached by the electron before it stop?
4. Capacitors
Is n electronic component use for storing electric charge and electric energy 1. Capacitance of Capacitor (C)
Capacitance of Capacitor can be determined by the equation as follows
According to gauss’s Law plates capacitor, the electric field strength between two plates can be determine as follows
With ε = ε0 εr
2. Electric Energy in Capacitor
The energy of capacitor can be determined by the equation blow:
3. Capacitor Connection a. Series Capacitor Connection
b. Parallel Connection of Capacitors
V
Q
C
d
A
C
0d
A
C
C
Q
QV
CV
W
2 22
1
2
1
2
1
n sC
C
C
C
1
....
1
1
1
2 1
n pC
C
C
C
1
2
...
Exercise 1. A parallel plates capacitor has the area of
each plate 2 cm2 and both are separated 0.2 cm. if the charge at each plate is 4 µC and ε0= 8.85 x 10-12 C2/Nm2 determine
a. capacitance of capacitor if the electric material is immersed between both plates (k = 4)
b. potential difference between both plates 2. Two capacitor 3 µC and 5 µC are connected
in series and set at a voltage source of 110 volt. Calculate the energy stored in that system
3. Two Capacitors C1 = 6 µC and C2 = 3µC are
connected in parallel and set at the voltage source of 18 V, calculate
a. substitute capacitance (Cp)
b. charge of q1 and q2
c. voltage V1 and V2
4. A capacitor has the capacitance of 0.6 µF, it is charged by voltage of 12 volt. Calculate the charges stored in the capacitor
5. A capacitor 6 µF is charged so that the voltage become 15 volt, then it is connected with capacitor 4 µF, calculate the voltage now
6. to store 1 C charge is used the capacitors which each has capacitance of 2.5 µF and it is connected in parallel with potential difference of 200 volt. Calculate the sum of capacitors used
7. To make the capacitance in the figure below equal to C2, determine the relation
between C2 and C1
8. A capacitor is given charges with voltage 100 volt. If the potential is reduced to 90 volt, calculate the decrease of energy in the capacitor
9. sebuah kapasitor yang dimuati oleh baterai 2 mV dapat menyimpan muatan 5.0 x 10-12 C. Tentukan kapasitas kapasitor tersebut 10. sebuah kapasitor keping sejajar memiliki
keping empat pesegi panjang dengan panjang 10 cm dan lebar 8 cm, dipisahkan oleh jarak 2 mm
a. hitunglah kapasitasnya
b. jika banyak muatan yang dipindahkan dari satu keping kekeping lainnya adalah 0.531 nC, berapa beda potesial kedua kepig tersebut itu?
11. sebuah kapasitor terbentuk dari dua lempeng almunium yang luas permukaannya masing-masing 100 cm2 dan dipisahkan oleh
minyak silikon yang tebalnya 1.00 mm a. tentukan kapasitas kapasitor ini b. tentukan muatan maksimum yang dapat
disimpan dalam kapasitor
12. sebuah kapasitor keping sejajar, luas tiap keping 2000 cm2 dan terpisah 1 cm satu saa
lain. Beda potensial diantara keping 3000 volt bila berisi udara, tetapi beda potensial itu menjadi 1000 volt ketika diantara keping disisipkan bahan dielectric. Hitungla : a. kapasitas mula-mula
b. muatan q pada tiap-tiap keping c. kapasitas C setelah penyisipan bahan dielectric
d. Permitivitas relatif εr bahan dielectric
e. permitivitas ε bahan dielectric
f. kuat medan listrik mula-mula E0 di antara
keping
g. kuat medan listrik E setelah penyisipan bahan dielektrik
13. Sebuah kapasitor keping sejajar terdiri dari dua keping. Luas tiap keping 200 cm2
dan dipisahkan oleh celah udara 4,0 cm a. hitnglah kapasitasnya
b. jika kapasitor dihubungkan pada baterai 500 v, berapakah muatan yang disimpan oleh kapasitor itu ?
c. tanpa melepas baterai, suatu cairan dengan εr= 2,50 dituangkan diantara
ruang antarkeping sehingga mengisi seluruh celah udara, berapakah kapasitas sekarang? Berapakah tambahan muatan yang akan mengalir dari baterai 500 volt menuju ke kapasitor ?
14. Tiga buah kapasitor 10,0 µF dan 5,00 µF dan 4 µF disusun seri dan ujung-ujungnya dihubungkan ke tegangan sumber 22 volt a. kapasitas ekivalen
b. muatan dan beda potensial tiap kkapasitor
15. Tiga buah kapasitor dengan kapasitas masing-masing 0.15 µF, 0,20 µF, 0,40 µF disusun paralel dan dihubungkan ke baterai 200 volt, tentukan
a. kapasitas dan muatan ekivalen b. muatan dan beda potensial tiap
kapasitor
16. Dua kapasitor 3 µF dan 5 µF disusun seri dan dihubungkan ke baterai 12 volt. a. tentukan energi yang tersimpan dalam
sistem
b. jika kedua kapasitor itu disusun paralel, berapakah kenaikkan energi yang tesimpan dala sistim ?
