# Physics Learning Center

## Electrostatics - Enrichment

physics.fisikastudycenter.com,- Electrostatics (Listrik Statis), enrichment problems for high school students grade 12, problem 1. This problem is taken from Indonesian colleges entrance examination.

Problem 1

Sebuah benda bermassa 20 gram dan bermuatan q = +0,5 µC digantungkan pada seutas tali ringan yang massanya dapat diabaikan. Tepat disebelah kanan benda pada jarak 15 cm diletakkan muatan q' = -1 µC yang menyebabkan posisi benda menjadi seperti gambar. Jika 1/4peo = 9 x 109 Nm2/C2 dan g = 10 m s-2, tegangan pada tali dekat pada harga .....Newton
A. 0,20
B. 0,24
C. 0,28
D. 0,32
E. 0,40
(Soal UMPTN 1995 Fisika)

Solution

We have three forces that are acting on q1, weight of q1, rope tension and Coulomb force. Find the weigth of q1 first:
W = mg = 20 × 10-3 (10) = 2 × 10-1 Newton

Coulomb force from interaction with q2
Fc = kq1q2/r2
Fc = (9 ×109)(0.5 ×10-6)(10-6)/(15 ×10-2 )2
Fc = 0.2 Newton

T = v[(Fc)2 + (W)2]
Insert your data and we get T = 0.28 N

Take a note that T , Fc and W are in equilibrium condition, so then T = Fc + W (in vectors sum symbol)

Prepared by fisikastudycenter.com
Sources/Literatures
-Soal UMPTN 1995

Problem 2
Two balls are tied with slight ropes of 25 cm of lengths. See the figure below. Each ball has 4 g of mass and q of electric charge. These balls are in equilibrium at ? = 74°. Find the charge at each ball, use acceleration due to gravity g = 10 m/s2, sin 37o = 0.6, cos 37o = 0.8, sin 53o = 0.8, cos 53o = 0.6

Dua bola kecil digantung dengan tali-tali sepanjang 25 cm seperti gambar di atas. Tiap bola memiliki massa 4 g dengan muatan masing-masing sama sebesar q. Kedua bola mencapai keseimbangan ketika ? = 74°. Tentukan muatan pada masing-masing bola, gunakan percepatan gravitasi bumi g = 10 m/s2

Solution

Three forces that are acting on each charges, see the figure below that is for the q on the rightside

We have rope tension (T), coulomb force (Fc) and the weight (W). These three forces are in equilibrium conditions. Get the distance between two charges (r) where r = 2d and d = l cos 53° see the figure:

r = 2 l cos 53°
r = 2 (25)(0.6) = 30 cm = 0.3 m

Apply the equlibrium conditions and get the components of tension rope (T) bring to x-y cartesian

y axis calculation
T sin 53° = W
T sin 53° = mg
T (0.8) = (4·10-3)10
T = 0.05 Newton

x axis calculation, insert the value of T that we already got

Prepared by fisikastudycenter.com
Sources/Literatures
-Marthen Kanginan, Bab 4 Medan dan Potensial Listrik, Fisika SMA 3A

Problem 3
Given four configured charges each has +q coulomb of electric charge and d meter of separation distance as below figure.

What is the coulomb force acting on point B charge show your answer in k, q and d!
Empat buah muatan tersusun seperti gambar di atas. Tiap muatan memiliki nilai +q C dan jarak pisah d meter. Tentukan gaya colulomb yang bekerja pada muatan yang terletak pada titik B, nyatakan jawaban dalam k, q dan d!
(Soal Listrik Statis - Fisika Study Center)

Solution

Redraw and include the forces and distances at point B

Charge B (+) and C (+), repel each other
FBC = kqBqC / r2 = kq2 / d2 = x

Charge B (+) and A (+), repel each other
FBA = kqBqA / r2 = kq2 / d2 = x

Charge B (+) and D (+), repel each other
FBD = kqBqD / r2 = kq2 / (d√2)2 = (1/2)x

FBA and FBC resultant (R1)
R1 = √[(FBA)2 + (FBC)2 ]
R1 = √[x2 + x2 ] = x√2 Newton

R1 must be in the same line as FBD cause of FBA = FBC so the θ of resultant is 45°

Finally the sum of R1 and FBD as the final result
F = R1 + FBD = x√2 + (1/2)x = (√2 + 1/2)x = (√2 + 1/2)( kq2 / d2 ) Newton

Prepared by fisikastudycenter.com
Sources/Literatures
-Marthen Kanginan, Bab 4 Medan dan Potensial Listrik, Fisika SMA 3A

Problem 4

Proton yang bergerak dari keping A ke B seperti terlihat pada gambar, memperoleh kecepatan 2 x 105 m s-1. Jika antara dua keping vakum, d = 1 cm, dan massa proton = 1,6 x 10-27 kg, muatan proton = 1,6 x 1019 C, maka beda potensial keping sejajar tersebut adalah...volt

(Soal UMPTN 1994 Fisika)

Solution

Using mechanic energy conservation law:

Prepared by fisikastudycenter.com
Sources/Literatures
-Soal UMPTN 1994 Fisika

Problem 5
An electron travels into two plates with speed of 105 m/s. The electric field between two plates is 104 N/C. Determine the value of d when the electron reaches the positive plate!

Diberikan dua buah keping sejajar seperti gambar. Sebuah elektron bergerak dengan kecepatan 105 m/s memasuki keping. Kuat medan listrik antara kedua keping adalah 104 N/C, tentukan nilai jarak d saat elektron mencapai keping positif!
(Fisika Study Center)

Solution

Consider the case as projectile motion, the horizontal distance d

Find the acceleration of electron in the plates caused of coulomb force

The vertical distance of electron to get the time for reaching the positive plate

Back to horizontal distance and get d

Prepared by fisikastudycenter.com
Sources/Literatures
-Halliday and Resnick, Fundamentals of Physics, Electric Field
-Marthin Kanginan, Medan dan Potensial Listrik, Fisika SMA Kelas 12

Electrostatics Problem 6

physics.fisikastudycenter.com,- Electrostatics (Listrik Statis), enrichment problems for high school students grade 12, problem 6.

Problem 6
Titik A terletak dalam medan listrik. Kuat medan listrik di titik A= 0,5 N C. Jika di titik A diletakkan benda bermuatan listrik 0,25 C, maka pada benda tersebut bekerja gaya Coulomb sebesar....
A. 0,125 N
B. 0,25 N
C. 0,35 N
D. 0,40 N
E. 0,70 N
(Soal EBTANAS Fisika Tahun 2000)

Solution
Electric field E = 0.5 NC–1
Electric charge q = 0.25 C
F = qE
F = (0.25)(0.5) = 0.125 N

Prepared by fisikastudycenter.com
Sources/Literatures
-Soal Ebtanas 2001

Electrostatics Problem 7

Problem 7
What must be the distance between point charge q1 = 25.0 μC and point charge q2 = −64.0 μC for the electrostatic force between them to have a magnitude of 3.60 N?
Tentukan jarak antara dua buah muatan titik q1 = 25,0 μC dan q2 = −64,0 μC agar gaya listrik statis antara kedua muatan sebesar 3,60 N !

Solution
Using the basic of electrical force formula

Prepared by fisikastudycenter.com
Sources/Literatures
-Halliday and Resnick, Fundamentals of Physics, Electric Field

Problem 8
Given 4 particles form a square of edge length d = 10 cm with charges q1 = −10 μC, q2 = +20 μC, q3 = −20 μC, and q4 = +10 μC. Find the net electric field produced by the particles at the square's center!

4 buah muatan membentuk suatu persegi dengan panjang sisi d = 10 cm. Keempat muatan masing-masing q1 = −10 μC, q2 = +20 μC, q3 = −20 μC, and q4 = +10 μC.Tentukan besar kuat medan listrik yang dihasilkan muatan-muatan tersebut pada pusat persegi!

Solution

These are the directions of electric fields that are produced by 4 charges. To simplify the calculations, find the sum E1 and E2, first find the distance of each charge to the center of square.

The distances are 0.5d√2

E1 and E3

E13 direction is the same with E3 direction.

E2 and E4

E24 in the same direction with E2

Finally the sum of E13 and E24 , E13 = E24 = x

(E13 and E24 forms an angle of 90o)
Proceed with the data, k = 9 x 109, μ = 10−6, r = 0.5d√2 and d = 10−1 m.

Prepared by fisikastudycenter.com
Sources/Literatures
-Halliday and Resnick, Fundamentals of Physics, Electric Field

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