# What is Coloumbs law: Definition and 20 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. ### I Question about Coloumb's law notation and math in two different textbooks

I am currently taking Electricity and Magnetism I for Graduate school and we are of course using Jackson Classical Electrodynamics 3e. I am used to Griffiths from undergrad and intro physics in that they describe it: But Jackson modifies the notation to include a cube of the magnitude in the...
2. ### Force between 2 point charges in VECTOR format (x i + y j + z k)

I tried using the distance between r2 and r1 and plugging them into the equation for i, j, k. >> So for the force in the x direction it was k*(4E-6*4E-6)/(4-9)^2. The answer I got was wrong according to webassign. Can someone please tell me what I am missing?
3. ### Net Electric field due to 3 charges

Homework Statement There is a 3nC charge at (-3,0), -6nC at (0,2) and 5nC at (1,0). What is the electric field at the origin (0,0)? Homework Equations ##E = \frac{Q}{4 \pi \epsilon_0 r^2}## The Attempt at a Solution i think its ##(\frac{1}{4 \pi \epsilon_0})(-\frac{14}{3} i - \frac{3}{2} j)##...
4. ### Coloumbs Law when have 3 charges at unknown distances

Homework Statement I have a question that I can't figure out. Question is "Two charges are fixed in location: charge q1 = +8e is located at the origin and charge q2 = -2e is located on the x-axis at x = L. At what point (other than infinitely away) can a proton (a unit positive charge e) be...
5. ### The net force on the charge placed at origin

Ques: If infinite number of charges placed along x-axis .At x=1, 1μC , x=2, 2μC, x=3, 3μC so on. Find the net force on charge 1μC placed at origin.Formula used (1/4πε)*q1*q2/r² Solved from this formula but stuck in a series
6. ### Coloumbs law question (checking answer)

Homework Statement Two spherical objects are separated by a distance of 2.5 x 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result each object...
7. ### Force on 3uC Charge - Solving Coloumb's Law Problem

Homework Statement Find force on 3uC charge. Homework Equations The Attempt at a Solution Assuming the 3uC charge is at point A and others are at point B and C FA = FAB + FAC FAB = K*(2*3)/5 FAC = K*(2*3)/5
8. ### Problem with Net Coulombic Force

Homework Statement Consider an ## n ##-dimensional solid sphere of radius ##R##, with uniform charge-density and a total charge ##Q##. A charged particle ##q## is kept at a distance of ##r## from the center. For ##r<R##, what is the Net Coulombic Force experienced by the particle? If it is in...
9. ### Potential of a Spherical Shell

Hi! I have trouble with solving this problem and would be really thankful for some help. :) 1. Homework Statement Inside a thin, spherical metal-shell with a radius of 50 cm, a smaller homogenous metal-sphere with a radius of 20 cm is placed concentrically. The smal sphere is grounded through...
10. ### Derivation of coloumbs law without Gauss's law

Whenever I try searching on how coloumbs law is derived Gauss's law is always used,for this reason when I search for Gauss's law it is always derived from coloumbs law :frown:.could you guys guys help me out by telling me which camfirst and how it was derived Coloumbs law- F=Q1Q2/r2ε Gauss's...
11. ### Coloumbs law with inverse cubic

1. Homework Statement A permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume s << r. a) Use the binomial approximation (1+x)-n ~= 1-nx if x << 1 to show that the net force exerted...
12. ### How Does Coulomb's Law Calculate Forces Between Two Point Charges?

Homework Statement Part 1: A charge of 2 µC is at the origin, and a charge of 6 µC is on the x-axis at x = 1 m. Find the force on charge q2. The Colulomb constant is 8.98755 × 10^9 N · m2/C2. Answer in units of N Part 2: Find the force on q1. Answer in units of N Homework...
13. ### How Do You Calculate Equilibrium Position Between Charges Using Coulomb's Law?

Coloumbs Law & Charges. Please help! :( Homework Statement A charge of +2.0 nC and a charge of +8.0 nC are separated by 36.0 cm. Find the equilibrium position for a −2.0 nC charge as a distance from the ﬁrst charge. Answer in units of cmHomework Equations q/r^2 The Attempt at a Solution I...
14. ### Coloumbs law and Newtons third law

Coloumbs law states that the force exerted by two charged particles on each other is given by f = kq1q2/d^2 Now say two charged particles (charge type irrelevant in question) x and y are d metres from each other then y exerts a force f on x. But since x is also exerting f on y then won't it...
15. ### Numericals On Electrostatics (including Coloumbs Law)

1. In hydrogen atom the distance between electron(e=1.6*10^-19 C)(Mass of electron=9.1*10^-31 kg) & proton(Mass Of proton=1.7*10^23 C) is 5.3*10^-11 m. 2. Calculate the electrical and gravitational forces between 2 particles 3. Can't do the problem... Please help!
16. ### Equilibrium of Charges using Coloumbs Law

Homework Statement A point charge of -0.5 C is located at the origin. A second point charge of 12 C is at x = 1 m, y = 0.5 m. Find the x and y coordinates of the position at which an electron would be in equilibrium. Homework Equations F=k*((q_1*q_2)/r^2) The Attempt at a Solution...
17. ### Clarification needed on coloumbs law, inverse square law, potential

I always try and think about the gravatational laws when thinking of the electrical ones: Can I just confirm that Electrical field strength in a uniform field = F/q (force per unit of charge) A electrical field strength at distance r from the body is \frac{-kQ}{r^{2}} where Q is the...
18. ### Atomic models and coloumbs law

Homework Statement The radius of the orbit of an electron in a hydrogen atom is 0.05 nm. Using the planetary model, calculate the orbital velocity needed by the electron to avoid being pulled into the nucleus by electrostatic attraction. Round up your answer to the nearest tenth...
19. ### Introductry Physics- Coloumbs Law problem

Homework Statement A small spherical insulator of mass 8.00x10^-2 Kg and charge 6.0x10^-5C is hung by a thin wire of negligible mass. A charge of -9.0x10^-5 is held 0.150 m away from the sphere and directly to the right of it, so the wire makes an angle with the vertical (see the drawing)...
20. ### Solve Coloumbs Law Problem: Mass & Charge of 2 Particles

Homework Statement Two equally charged particles are held 3.2x10^-3 m apart and then released from rest. The initial acceleration of the first particles is observed to be 7.0m/s^2 and that of the second to be 9.0 m/s^2. If the mass of the first particle is 6.3x10^-7 kg , what are a.) the...