# What is Coulomb's law: Definition and 403 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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18. ### Coulomb's Law and Conditional Convergent Alternating Harmonic Series

Mary Boas attempts to explain this by pointing out that the situation cannot arise because charges will have to be placed individually, and in an order, and that order would represent the order we sum in. That at any point the unplaced infinite charges would form an infinite divergent series...
19. ### Three positive point charges are located on a line (Coulomb's Law)

I need some help resolving the follow problem. I really don't know where to put the "twice as large as the resultant force on Q3" in order to build an equation. Thank you !
20. ### Deriving Pith Ball Mass from Coulomb's Law: A Scientific Exploration

I actually found most of it out I'm just struggling with how to find the mass of the balls. I'm not sure how you would do that since could only derive two equations from the information given or are we assuming the mass is so small that it doesn't matter? Q = charge of one pith ball d =...
21. ### Coulomb's Law problem: Force of attraction between the two singly charged ions

In a salt crystal, the distance between adjacent sodium and chloride ions is 2.82×10^−10m. What is the force of attraction between the two singly charged ions?
22. ### Test charge velocity in Coulomb's Law

The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of...
23. ### Coulomb's Law: Solving Problems with Electric Charges

This is my attempt but they said my answer is wrong
24. ### Find the electric field on the surface of a sphere using Coulomb's law

Note that the solution is 5625 V/m in z direction which is found easier using Gauss' law, but I want to find the same result using Coulombs law for confirmation. Lets give the radius 0.04 the variable a = 0.04m. ##\rho## is the charge distribution distributed evenly on the surface of the...
25. ### The relationship of one of Maxwell's equations to Coulomb's Law

My textbook tells me that one of Maxwell's equations, namely divergence of E = 4pi * charge density (in cgs) or divergence of E = pi / epsilon nought (in SI) is exactly equivalent to Coulomb's Law. How in the world is that so? Any ideas would be appreciated.
26. ### MHB Coulomb's Law: Find Force of 4.0 & 6.0 $\mu C$ Charges

$\tiny{18.3.6 Coulomb's Law }$ $\text{A charge of$q_1=4.0 \mu \, C$is at origin, and charge}$ $\text{$q_2=6.0 \mu \, C$is on the x-axis at$x=3.0 m$}$, $\text{(a) find the force on the charge$q_2$}$ $\text{(b) find the force on$q_1$}$ \$\text{(c) how would your answer for parts (a)...
27. ### Coulomb's Law: The distance between two charged spheres

The force of the sphere increases because according to Coulomb's force increases as the distance decreases. I'm not sure if this is correct.
28. ### 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...
29. ### 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...
30. ### Coulomb's Law and 4 point charges

A charge Q is placed at the centre of the square of side 2.90 cm, at the corners of which four identical charges q = 6.5 C are placed. Find the value of the charge Q so that the whole system is in equilibrium. Can someone help me figure out where I have went wrong, I began by finding the force...
31. ### Dependence of Coulomb's law on the medium

Homework Statement I read in my textbook that the force exerted by a charged particle q1 on another charged particle q2 does not depend on the medium between them. Yet we multiply ε by ε(r) in coulomb's law when there is a medium present between the particles. Can someone please explain this...
32. ### Why we don’t put a minus sign in Coulomb's law

While calculating the force between two charges , why we don't put minus sign with charge.
33. ### Calculating Charge and Force Using Coulomb's Law and Trigonometry

Homework Statement Two small balls, each of mass 5.0 g, are attached to silk threads 50 cm long, which are in turn tied to the same point on the ceiling, as shown below. When the balls are given the same charge Q, the threads hang at 5.0° to the vertical, as shown below. What is the magnitude...
34. ### Coulomb's Law and charge quantization

Coulomb's law states that the force between particles depends on their charge. But protons and electrons have equal but opposite charges. Shouldn't the formula simply have constants with the only changes required being the signs?
35. ### 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]
36. ### Coulomb's Law Grade 12 Question -- Net Electric Field affecting a Charge

Homework Statement Examine the charge distribution shown. b) What is the net electric field acting on charge 1? Homework Equations I used the equation E= (kq1/r^2) + (kq2/r^2) The Attempt at a Solution I subbed 9.0 x 10^9 in for k, 3.0 x 10^-5 for both q1 and q2, and 2m for r. My final answer...
37. ### Question regarding Coulomb's Law

Homework Statement Three separate spheres next to each other. The one on the left is positive (charge of +25.5μ C). The one on the right is negative(-25.5μ C). The two are separated by 0.25m. The third sphere has a charge of +2.5μ C and is placed exactly halfway between the two. Find the force...
38. ### 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...
39. ### Three particles, finding Q of one of them (Coulomb's Law)

Homework Statement "A particle with charge -3.03 nC is at the origin, and a particle with negative charge of magnitude Q is at x = 49.0 cm. A third particle with a positive charge is in equilibrium at x = 20.8 cm. What is Q?" Homework Equations I'm fairly certain that Coulomb's Law is the...
40. ### Coulomb's law, electrostatics?

Equation: ΣF=Σk(qi)(qj)/(r^2) Question: Considering more than a couple of particles. How can a net force on a charged particle be calculated if Coulomb's law is under the restriction of static forces? Thanks!
41. ### 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...
42. S

### 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...
43. M

### Force of Gravity & Coulomb's Law Force Question

Homework Statement Two small spheres of 15 g each are suspended from a common point by threads of length 35 cm. Each thread makes an angle with the vertical of 20 degrees. Each sphere carries the same charge. Find the magnitude of this charge. (The correct answer is: 0.58 μC)Homework Equations...
44. P

### 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°...
45. P

### 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...
46. ### What is the Electric Flux through a Net in a Uniform Electric Field?

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...
47. ### Coulomb's Law in 3D: Find Electric Force & Field

Homework Statement q1= 5 x 10^-6C position (1;2,-1) q2= -3 x 10^-6 C position (-2,1,3) a) what is the electric force caused by q2 on q1? (vector notation) b) what is the electric field at (0,0,0) Homework Equations F = kq1q2/r^2 E= F/q The Attempt at a Solution I really don't...
48. ### Coulomb's law without a pure inverse square relationship?

Then it goes on explaining how Gauss law would fail because for a very large surface, E field would be vanish with flux through it and though we can calculate div for this field it won't depend on source density. But I don't get what makes this particular function so evil that it would break...
49. ### Coulomb's law; vector form problem

Homework Statement 3 charges are placed like shown: Q1 __4cm____ Q2 ______6cm___________Q3 Q1=-2nC Q2= 1nC Q3= 3nC Find the resultant force and its direction upon the charge Q3. Homework Equations F=k0*(Q1Q2)/r2 k0-constant, equals to 9*10^9 r-distance The Attempt at a Solution...
50. ### 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...