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 1/4πεo = 9 x 109Nm2/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 = √[(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)

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 θ = 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 θ = 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

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

Rmust 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

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:

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