# Coulomb's law Definition and 40 Discussions

Coulomb's law, or Coulomb's inverse-square law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The law was first discovered in 1785 by French physicist Charles-Augustin de Coulomb, hence the name. Coulomb's law was essential to the development of the theory of electromagnetism, maybe even its starting point, as it made it possible to discuss the quantity of electric charge in a meaningful way.The law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them,

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{\displaystyle |F|=k_{\text{e}}{\frac {|q_{1}q_{2}|}{r^{2}}}}
Here, ke is Coulomb's constant (ke ≈ 8.988×109 N⋅m2⋅C−2), q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges.
The force is along the straight line joining the two charges. If the charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive.
Being an inverse-square law, the law is analogous to Isaac Newton's inverse-square law of universal gravitation, but gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. Coulomb's law can be used to derive Gauss's law, and vice versa. In the case of a single stationary point charge, the two laws are equivalent, expressing the same physical law in different ways. The law has been tested extensively, and observations have upheld the law on the scale from 10−16 m to 108 m.

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1. ### Force between point charges at the center of two spherical shells

If these point charges were placed in vacuum without any spherical shells in the picture, then the force between these charges would be ##F =\dfrac { k q_1 q_2} {d^2}##. But, I am unable to reason how spherical shells would alter the force between them. I do know that if charges were on the...
2. ### MIT OCW, 8.02, Electromagnetism: Charged Cylindrical Shell

Here is figure 2.16.6 Here is the picture I drew to set up the problem My first question is if the reasoning and integrals are correct. I used Maple to compute the three integrals. The first two result in 0, which makes sense by symmetry. Maple can't seem to solve the last integral.
3. ### The time for a proton to reach a certain velocity

A nuclear reactor is built to fuse two hydrogen atoms that are already ionized to protons. However, the electric field of the protons are becoming a significant obstacle. If the reaction was to be defined as H2--> 2H++2e-, if the mass of a proton is mp, the radius of a proton r the charge of an...
4. ### Force acting on a charge across a hybrid medium

The force on charge ##q_2## will depend on the electric field in medium with dielectric ##K_2##. Electric field in this second dielectric due to ##q_1## is ##E = \dfrac {kq_1} {K_2r^2}## where r would be the distance from ##q_1##. So, the electric field at the point where charge ##q_2## is...
5. ### Expression for the magnitude of an electric field

k(q_1-q_2)/(R^2+x^2)^3/2
6. ### Help with Coulomb's law: Net electrostatic force

I tried just calculating the force with Coulomb's law, then calculating the forces for each vector individually and adding, but I got it wrong both ways
7. ### How do I calculate the ratio of forces between two conducting spheres?

Here are the answer choices: a) F1 = 2F2 b) F1 = 8F2 c) 2F1 = F2 d) F1 = 4F2 e) F1 = F2 I figured that Coulomb's law would tell us the magnitude of the forces are identical, so I answered E, but that was incorrect. (Screenshot of question attached)
8. ### Electrostatics - Coulomb's Law

Homework Statement The magnitude of the electrostatic force between point charges ##q_1 = 26~\mu C## and ##q_2 = 47~\mu C## is initially ##F_1=5.70~N##. The separation distance between the charges, ##r_1## is then changed such that the magnitude of the force is, ##F_2=0.57~N##. (a) What is the...
9. ### Find the electric field of a point outside sphere

Homework Statement Find the electric field of a point outside sphere without using Gauss's law. (Do not evaluate the integral) Homework Equations Coulomb's Law Spherical Co-ordinate System The Attempt at a Solution I have attached my attempt as a picture but now I am stuck, I don't know how I...
10. ### Help with Coulomb's law problem

Homework Statement The correct answer is 20.3 kg, but I got 23.4 kg. What did I do wrong here? Please refer to part 3 for the problem question. Homework Equations Refer to part 3. The Attempt at a Solution [/B]
11. ### Apparent disagreement between Coulomb's Law and Gauss' Law

This is probably my misunderstanding, so please clarify. In a region of empty space, there are two point charges with the charges+Q and -Q. Exactly in the middle of the two charges (distance r from both charges) is point P, colinear with the centers of both charges. A Gaussian surface that...
12. ### Modification in Coulomb's Law and its implications

If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship, How would it affect an isolated charged conducting sphere? How would it's field vary within the volume and how would the volumetric charge density be affected? Please give in some...
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### Coulomb's Law, Three Charges, X Y Components, Angle

Homework Statement This is finding net force on Q3. I was taught by my Physics teacher to always get angle from the Positive side of x-axis (+X-Axis). For example in the above situation, if the angle is -30deg from the +x-axis (assuming the Q3 is the origin), Why is F31 x-component = 140...
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### Component Force on a 1.0 nC Charge

Homework Statement What is the force F on the 1.0 nC charge at the bottom in the figure? Give your answer in component form. In the figure, the +!.0 nC charge is adjacent to a +2.0 nC charge to the left at a 45° angle, a -6.0 nC charge directly above, and a -2.0 nC charge to the right at a 45°...
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### Magnitude and Direction of the Force on a Charge

Homework Statement What is the force F (a vector) on the -10 nC charge in the figure? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x-axis. The figure shown is in the shape of a rectangle. On the top left is a +15 nC charge; on the top right is a...
16. ### Electric Flux through a Net

Homework Statement [/B] A butterfly net hangs from a circular loop of diameter 400 mm . You hold the loop horizontally in a region where the electric field is 150 N/C downward, as shown in (Figure 1) . What is the electric flux through the net? Homework Equations k = 9E9 N E = kq/r2 Flux = Q...
17. ### Coulomb's Law problem: Charged particles and the net electric field and force

Homework Statement Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 19e. Particle 3 of charge q3 = +16e is initially on the x axis near particle 2.Then particle 3 is gradually moved in the positive direction of...
18. ### Coulomb's Law in Two Dimensions

Homework Statement Three charges, q1, q2, and q3, lie in a plane, as shown below. Find the net force on charge q2 (please refer to attachment for diagram) Homework Equations F= k x q1q2/R^2, knowledge of trig functions and separating x and y components The Attempt at a Solution So I found the...
19. ### Measuring charge (or potential) with electroscope?

I am trying to measure the charge(or voltage) of a positively charged sphere by touching it with a non- calibrated electroscope. I am getting consistent results in the separation(or angle) between the metal leaves, but I don´t know how to calculate the voltage between the leaves from there. I...
20. ### Is the total electric field of two opposite charges 0?

Let's say you have two particles that are the same in magnitude but have opposite charges like the equation down below: E1 = -q*k/r^2 E2 = q*k/r^2 ETotal = q*k/r^2 + -q*k/r^2 = 0 Does this mean that the electric field of both these charges cancel out each other? Then what is the electric...
21. ### Consider the configuration consisting a +q charge....

and two -q charges aligned along the x-axis as follows... -q__________q__________-q <--- the space between them being d a) Suppose the +q charge is displaced perpendicularly by a small vertical distance dy. What is the total force F acting on it? Taylor expand your answer to leading order in...
22. ### Finding the Electric Field at the Midpoint of two rings

Homework Statement Hello, Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to -22 nC and the right ring is charged to +22 nC . What is the magnitude of the electric field E⃗ at the midpoint between the two rings? Homework Equations [/B] E = Kq/r^2 K =...
23. ### E-field of a Semi-spherical charge distribution with a hole

Homework Statement Using direct integration, compute the electric field at the point (0,0,Z) of a semi-espherical (z > 0) charge distribution of radius R < Z and density ##\rho=constant## having a spherical hole of radius ##r_h<R## centered at (0,0,##r_h##). Homework Equations Coulomb's law...
24. ### Finding number of charges using Coulomb's Law

Homework Statement Please refer to the image; problem-1. My theory is that there are two spheres 'A' and 'B', where 'A' is (partially and primarily) positively charged, and 'B' is (partially and primarily) negatively charged. The magnitude of negative charge is greater than the positive charge...
25. ### Justification for the acceptance of Coulomb's law

I read the Coulomb's first memoir on Electricity and Magnetism (Louis L. Bucciarelli english translated version), and found it to contain only three trials (as complained by many) to reach the conclusion of a 1/r2 equation for the force. And many seems to have also complained for not having able...
26. ### How a particle knows about the existence of another particle

Hello, I have a question about the interaction between particles. Maybe it's a simple question, but it's bothering me. Consider Coulomb's law. From Wikipedia we have a simple definition to illustrate: "The magnitude of the electrostatic force of interaction between two point charges is directly...
27. ### Coulomb's Law of Electric Displacement -- Why is there none?

Why is there no Coulomb's Law for the electric displacement?
28. ### Net force on particle 1 due to particle 2 in vector form?

Homework Statement Hi all, I have this quiz on MasteringPhysics, but I can't seem to get the right answer.[/B] Consider two positively charged particles, one of charge q0 (particle 0) fixed at the origin, and another of charge q1 (particle 1) fixed on the y-axis at (0,d1,0). What is the net...
29. ### Can you merge these equations and get acceleration

m*a=k*Q1*Q2/r equalizing Newton's first law and coulomb's force to get acceleration of the specific charged body.
30. ### Magnitude and Direction of an (E) Electric field of a square

Homework Statement What is E in Magnitude and Direction at the center of the square of (fig. 3-7). Assume that q = 10x10-8 C and a = 5 cm Now I have am not well versed with vectors, I don't like them and they don't like me. I can not figure out the directions the magnitudes move in...
31. ### How Coulomb's Law relates to generators? (voltage)

Homework Statement In science class, we are supposed to explain how a generator works and functions. However, we have to incorporate coulomb's law in our explanation. Homework Equations F=kQ1Q2/r^2<-- coulomb's law The Attempt at a Solution How I understood it was that a generator consists of...
32. ### How did Coulomb charge his spheres to verify Coulomb's law?

We are doing an experiment to verify coulomb's law, and we are currently using a stable voltage source. However, we were assigned to do it using static electricity, and we were wondering how to establish inverse r^2 dependence if the amount of the charge on the ball isn't the same every time we...
33. ### Analytical Problem with Coulomb's Law

Homework Statement Consider a parallel universe where the laws of nature as we know them are different, and aqueous solutions can have an excess charge. Two beakers are separated 1.20 meters and each contains 0.300 L of an aqueous solution of 6.40 × 10-6 M excess charge. One beaker has a net...
34. ### Decomposition of a Carbonate

Homework Statement http://i.imgur.com/Ypqcw19.png Homework Equations N/A The Attempt at a Solution Since the reaction involves the breaking of bonds in MCO3, I assume we are looking at coulomb interactions. I'd think the answer is D) BaCO3 because all the options have a 2+ charge, but barium...
35. ### Three point charges with a central fourth charge

Homework Statement It is the last part, part (c) that I'm having trouble with, but I'll post the entire question for clarity. Three charges (q) form the vertices of an equilateral triangle. A fourth charge Q ( Q = -q ) is placed at the center of the triangle. (a) will the charges at the...
36. ### Coulomb's law vs. Newton's law of gravitation?

What would be the easiest way to describe the similarities and differences between the two laws, other than the fact that their formulas are built similarly and they use different measurements. Any input would be great; I am currently having a brain block! Coulombs Law:F=K (q1*q2)/r^2 Newtons...
37. ### Question about Coulomb's law

Hi, I'm having trouble figuring out one of my homework questions. It says " The total charge on two charged objects is Q. What must the charges on each of them be, in order that the force between them is (a) maximum and (b) minimum. Thanks guys.
38. ### Simple application of Coulomb's Law/Equation

Homework Statement Two pieces of copper weighing 10 grams each are 10 cm apart and 1/1000 electrons are transferred from one to the other. Find the force of electrostatic attraction between them. Homework Equations [/B] Molar mass Cu: 63.5 g/mol \frac{1}{4\pi \epsilon_0} = 9 \times 10^9...
39. ### Validity of application of Coulomb's Law with moving charge?

Hi there, I'm trying to brush up on some of my E&M and am comparing treatments of Coulomb's Law in introductory calculus-based texts with higher level material. My understanding was that Coulomb's Law (and by extension, calculation of the electrostatic force on a charged particle using F = qE)...
40. ### How to find the magnitude of a point charge given 2 others?

Homework Statement Three charges are placed as shown in the figure below. The magnitude of q1 is 2.00 µC, but its sign is not known. The charge and sign of q2 is not known. We do know that q3 is +4.00 µC and the net force on q3 is entirely in the negative x-direction. a.) Deduce the signs of...