Fisika Study Center

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
F_c = ^kq₁q₂/_r²
F_c = ^{(9 ×109)(0.5 ×10-6)(10-6)}/_{(15 ×10^-2 )²}
F_c = 0.2 Newton

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

Take a note that T , F_c and W are in equilibrium condition, so then T = F_c + 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 37^o = 0.6, cos 37^o = 0.8, sin 53^o = 0.8, cos 53^o = 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
F_BC = kq_Bq_C / r² = kq² / d² = x

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

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

F_BA and F_BC resultant (R1)
R₁ = √[(F_BA)² + (F_BC)² ]
R₁ = √[x² + x² ] = x√2 Newton

R₁ must be in the same line as F_BD cause of F_BA = F_BC so the θ of resultant is 45°

Finally the sum of R1 and F_BD as the final result
F = R₁ + F_BD = 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 90^o)
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