Electric Forces: Coulomb’s Law Help

In summary, two identical small spheres of mass 2.0 g are suspended by a hook in the ceiling from the centre of an insulating thread of length 0.60 m. The spheres are given identical electric charges and hang in static equilibrium at an angle of 30.0° between the string halves. Using the equations FE = kq1q2/r2 and F2 = F1 (q a2/ q a1) (q b2 / q b1) (r1/r2)2, where k = 9.0 x 109 Nm2/C2, the magnitude of the charge on each sphere can be calculated to be 4 x 10 -13 C. In order to
  • #1
dark.light
2
0

Homework Statement



Two identical small spheres of mass 2.0 g are fastened to the ends of an insulating
thread of length 0.60 m. The spheres are suspended by a hook in the ceiling from
the centre of the thread. The spheres are given identical electric charges and hang
in static equilibrium, with an angle of 30.0° between the string halves. Calculate the magnitude of the charge on each sphere.

Homework Equations



FE = kq1q2/r2

F2 = F1 (q a2/ q a1) (q b2 / q b1) (r1/r2)2

k = 9.0 x 109 Nm2/C2

The Attempt at a Solution



So we have to find the q. I believe it should be the same since same mass, same angle from the normal line, 15 degrees and they have the same length, 0.6m. So if it is possible to find one of them, it is possible to find the other.

If I figure out something else for it, I will post/update this post, thanks for the help.


The final answer should be: 1.2 x 10-7 C
 
Last edited:
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  • #2
Hi dark.light, welcome to PF.
In the equilibrium position identify the forces acting on the individual charged spheres.
Resolve them into vertical and horizontal components.
Then equate ΣFx = 0 and ΣFy = 0. Then solve for F.
 
  • #3
k. So:
Fx = mg cosx = (0.002kg)(9.8N/kg) cos 15 = 0.0189 N
Fy = mg cosx = (0.002kg)(9.8N/kg) sin 15 = 0.00507 N

sum of F = 0.019664 N = 0.020 N

FE = kq1q2/r2
0.020 N = (9.0x109 C)q1q2 / (0.6m)2
q1q2 = 8 x 10 -13
q = 8 x 10 -13 / 2
= 4 x 10 -13

but still, I get the answer different. Did I do something wrong?
 
Last edited:
  • #4
On each charged sphere three forces are acting.
i) Horizontal electrostatic repulsive force
ii) Vertical weight of the sphere
iii) Tension in the string making an angle θ with the vertical.
Now find ΣFx and ΣFy.
 

Related to Electric Forces: Coulomb’s Law Help

1. What is Coulomb's Law and how does it relate to electric forces?

Coulomb's Law is a fundamental law in electromagnetism that describes the relationship between electric charges and the force they exert on each other. It states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This means that the larger the charges and the closer they are, the stronger the force will be.

2. How is Coulomb's Law different from Newton's Law of Universal Gravitation?

Coulomb's Law and Newton's Law of Universal Gravitation are both inverse-square laws, meaning the force between two objects decreases as the square of the distance between them increases. However, Coulomb's Law deals with electric charges, while Newton's Law deals with masses. Additionally, the force in Coulomb's Law can be repulsive or attractive, depending on the signs of the charges, while the force in Newton's Law is always attractive.

3. What is the unit of electric force in Coulomb's Law?

The unit of electric force in Coulomb's Law is the Newton (N), which is equal to kg*m/s^2. This unit is derived from the fundamental units of charge (C), distance (m), and mass (kg) in the equation for Coulomb's Law.

4. Can Coulomb's Law be used to calculate the force between multiple charges?

Yes, Coulomb's Law can be used to calculate the force between multiple charges by using the principle of superposition. This means that the total force on a charge due to multiple charges can be found by summing up the individual forces between that charge and each of the other charges.

5. How is Coulomb's Law used in everyday life?

Coulomb's Law has many practical applications in everyday life, such as in the operation of electrical devices and the behavior of electrically charged particles. It is also used in industries such as electronics, telecommunications, and energy production. Additionally, understanding Coulomb's Law is crucial for the design and functioning of electrical circuits and systems.

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