What is Coulomb's law: Definition and 403 Discussions
Coulomb's law, or Coulomb's inversesquare 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 CharlesAugustin 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,

F

=
k
e

q
1
q
2

r
2
{\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 inversesquare law, the law is analogous to Isaac Newton's inversesquare 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.
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...
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...
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...
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...
This is SAMPLE PROBLEM 257 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...
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...
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.
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...
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...
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...
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...
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
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)
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...
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!
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...
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...
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 !
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 =...
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?
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...
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...
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.
$\tiny{18.3.6 Coulomb's Law }$
$\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 xaxis 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)...
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...
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 Coordinate 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...
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...
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...
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...
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?
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]
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...
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...
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...
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...
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!
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...
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 xaxis (+XAxis).
For example in the above situation, if the angle is 30deg from the +xaxis (assuming the Q3 is the origin),
Why is F31 xcomponent = 140...
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...
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°...
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 +xaxis.
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...
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...
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...
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...
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
k0constant, equals to 9*10^9
rdistance
The Attempt at a Solution...
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...