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,















{\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. A

    Importance/Use of Gauss' Law and Ampere's Circuital Law

    So the question is like I mentioned. I know how to use GL and ACL in place of CL and BSL. I also know that they make the calculations simpler. The problem is whenever GL and ACL are used in place of CL or BSL, they are used in the following way: Gauss Law:$$\int{ E...
  2. DanielGuh

    Coulomb's Law Application: A charge repelling a mass on a frictionless incline

    Fg = Fc Fg = 2.3g*9.8m/s^2*cos(28)=19.90N 19.90 = (8.99*10^9)*(4*10^-6)*(6*10^-6)/(r^2) 1/(r^2) = 92.23 r = 0.104m However, it's not one of the option...
  3. LarryS

    I Coulomb’s Law in a Moving Reference Frame

    In classical electromagnetism, Coulomb’s Law gives the force between two stationary charged particles, a certain distance apart. It is an inverse square law – the density of the electric field lines is spherically symmetric. What if the same two charged particles are moving in parallel, say to...
  4. paulimerci

    Find the magnitude of the electric force from 3 charges at vertices of a cube

    There are three charges with +1 μC and −1 μC, are placed at the opposite corners of a cube with edges of length 1 cm, and the distance from P to B is 1cm 2. I labeled them as A, P, and B, which is shown in the diagram below. Since we need to find the magnitude of the charge at point P and the...
  5. mangofan

    I Electrostatic force exerted on an electron inside a nucleus

    This is SAMPLE PROBLEM 25-7 from "Physics" by Resnik, Halliday, and Krane, in the chapter "Electric Field and Coulomb's Law". After describing the behavior of uniformly charged spherical shells: follows a sample problem: The solution to (a) goes to say that the volume inside R/2 is 1/8 of the...
  6. V

    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...
  7. Z

    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.
  8. Y

    Coulomb's law — A negative charge balanced between 3 positive charges

    hello i would like to understand something, i found the right answer but there is still something i don't understand. here is the figure and here is my correct solution what i don't understand is why F(3,Q) is 3kQ/r^2 i mean why is the 3? i only calculat the force between q3 and Q so why...
  9. K

    I Coulomb's law for steady currents

    If I've steady currents i.e ##\frac{\partial}{\partial t} J=0## , does coulombs law hold in this case to find the electric field? Since this isn't the case of electrostatics so it might not hold, but if we look at the charge density it is the same for all time, this suggests that the charges...
  10. dirb

    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...
  11. V

    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...
  12. M

    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
  13. S

    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)
  14. Mayan Fung

    I How is Coulomb's Law compatible with quantum physics?

    In classical physics, we treat an electron as a point charge with a Coulomb potential ## V = \frac{q}{4\pi\epsilon_o r}##. However, in quantum mechanics, we treat it as an electron cloud. In this situation, how shall we describe the Coulomb potential? Shall we treat the electron as a charge...
  15. X

    Is Coulomb's law valid in a non-inertial frame?

    Hi, I was wondering, if the charges do not move in a non inertial frame and I don't move too in this frame, will I see the same Coulomb force, some fictitious forces and radiation coming from these static charges? Thanks!
  16. Efeguleroglu

    How does permittivity in Coulomb's law work?

    Coulomb's Law $$ \vec{F} = \frac{1}{4 \pi \epsilon} \frac{q_1 q_2}{r^2} \hat{r} $$ $$ \vec{E} = \frac{1}{4 \pi \epsilon} \frac{Q}{r^2} \hat{r} $$ Let's say we want to find electric field with a distance r from charge Q. How does permittivity effects the magnitude? Will I choose the permittivity...
  17. P

    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...
  18. M

    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 !
  19. kashika1212

    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 =...
  20. S

    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?
  21. A

    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...
  22. Z

    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...
  23. M

    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.
  24. karush

    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)...
  25. V

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    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.
  26. WhiteWolf98

    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...
  27. C

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  28. J

    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...
  29. Krushnaraj Pandya

    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...
  30. Zain580

    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.
  31. C

    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...
  32. A

    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?
  33. A

    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]
  34. David John

    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...
  35. K

    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...
  36. S

    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...
  37. S

    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...
  38. Jurtinus

    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!
  39. Aastik Tripathi

    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...
  40. 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...
  41. 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...
  42. 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°...
  43. 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...
  44. Sunbodi

    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...
  45. S

    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...
  46. B

    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...
  47. D

    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...
  48. L

    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...