What is Point charge: Definition and 363 Discussions

A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space. A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. A point particle can also be referred in the case of a moving body in terms of physics.
In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge.Sometimes, due to specific combinations of properties, extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in 3-dimensional space whose interactions are described by the inverse square law behave in such a way as if all their matter were concentrated in their centers of mass. In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. For example, the atomic orbit of an electron in the hydrogen atom occupies a volume of ~10−30 m3. There is nevertheless a distinction between elementary particles such as electrons or quarks, which have no known internal structure, versus composite particles such as protons, which do have internal structure: A proton is made of three quarks.
Elementary particles are sometimes called "point particles", but this is in a different sense than discussed above.

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  1. ARoyC

    Total Force on a Point Charge in Motion

    As the observer is moving, there will be a magnetic force. Electric Field of the Rod = λ/2πεr r̂ Electric Force on the Point Charge = qλ/2πεr r̂ Magnetic Force on the Point Charge = q(vxB) = qvB n̂ = qv(µI/2πr) n̂ = qv(µλv/2πr) n̂ = µqλv²/2πr n̂ Total Force = Electric Force + Magnetic Force
  2. L

    Divergence of the Electric field of a point charge

    Hi, unfortunately, I am not sure if I have calculated the task correctly The electric field of a point charge looks like this ##\vec{E}(\vec{r})=\frac{Q}{4 \pi \epsilon_0}\frac{\vec{r}}{|\vec{r}|^3}## I have now simply divided the electric field into its components i.e. #E_x , E-y, E_z#...
  3. Spinnor

    I De Broglie–Bohm theory scattering from point charge, paths

    I think I read somewhere that the trajectories of particles in the De Broglie–Bohm theory do not cross, is that true? If true, then in the case of Rutherford scattering the trajectories below can't be those of the De Broglie-Bohm theory? Thanks.
  4. bryanso

    B Static Point Charge Should Have Zero Effect

    How can we detect electrical effect of a static point charge at all? I think of a point charge like a sea urchin. With field lines going outwards in all directions (for +ve). So the vector pointing at me directly should be canceled perfectly by the vector going away from me. And so each line...
  5. K

    I Retarded potential of a moving point charge

    Potential of a moving point charge is given as ##V (\mathbf r,t)= \frac{1}{4\pi\epsilon_0}\int \frac{\rho (\mathbf r',t_r) }{|\mathbf{ (r-r')}|}d\tau'## Griffiths says: " It is true that for a point source the denominator ## |\mathbf{(r-r')}|## comes outside the integral..."Why does it come...
  6. J

    Electric Field Inside a Gaussian Surface with Point Charge q

    If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...
  7. guyvsdcsniper

    Method of Images for a single point charge in a capacitor

    Disclaimer: This is not a repost. The problem wants me to calculate the force of a p.c. , that is isolated by itself (this p.c. is the only charge this problem starts with in this problem) inside a capacitor, a distance h/4 from the bottom plate. This is what I have though of so far but I...
  8. guyvsdcsniper

    Point charge in cavity of a spherical neutral conductor

    For (a) this problem, the only thing I can see changing is the distribution of the negative charge on the inner wall of the cavity. When the point charge is in the center of the cavity, you could say the induced charged is spread symmetrically on the inner cavity wall in order to oppose the...
  9. guyvsdcsniper

    Electric Field acting on a point charge

    I believe I have all parameters set up correctly to evaluate part A of this problem but I am unsure of the bounds. I can't integrate from 0 to R because that part of this sheet has a hole there. I need to integrate from R to the other end of the sheet. Im not sure how I would figure out the...
  10. F

    Engineering Finding the force acting on a point charge with a disk around it

    Question: Here's my attempt with the relevant equations: The correct answer is F = -99.4 az μN. Could someone please figure out my mistake?
  11. P

    Equilibrium circular ring of uniform charge with point charge

    This is an offshoot of @Angela G 's thread. I don't want to hijack her thread so I decided to create a new one. Original thread https://www.physicsforums.com/threads/unstable-or-stable-electrostatic-equilibrium.1007881/ @kuruman @PeroK @bob012345 If you have the time I'd appreciate your input...
  12. D

    Potential outside a grounded conductor with point charge inside

    Potential inside is given as in ,https://en.wikipedia.org/wiki/Method_of_image_charges, which is the sum of excitation and induced potential. When the charge is outside it is easy to argue potential is zero in the sphere. But when we have charge inside and image outside, what is potential...
  13. S

    Point charge near charged plate

    I thought the equation listed should be used, with the 'charge density' determined by the point charge multiplied by the area of the plate, but not sure if that makes sense.
  14. willDavidson

    Electric field of a point charge

    I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?
  15. wcjy

    Electric field problem using Gauss' law: Point charge moving near a line charge

    F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so...
  16. Hiero

    Magnetic field of a point charge moving uniformly

    Everywhere I look online I see the formula for the magnetic field of a uniformly moving charge is, $$\frac{\mu_0 q \vec v \times \vec r}{4\pi r^3}$$ but when I calculate it by transforming the electrostatic field (taking the motion along x) I get, $$\frac{\gamma \mu_0 q \vec v \times \vec...
  17. M

    Electric Field of Point Charge at y=r and an Infinitely Long Cylinder

    Let point charge q be at y=r. Let there be an infinite conducting plane along the x-axis and z-axis that is neutrally charged. In this case, the method of mirror charges can be used. The plane is replaced by a point charge -q at y=-r. The electric field for y > 0 is the same in both cases...
  18. Z

    Electric field direction on a grounded conducting sphere

    I am required to find the direction of the electric field on the surface of a grounded conducting sphere in the proximity of a point charge ##+q##. The distance between the center of the sphere and the point charge is ##d## and using the method of images we find that the charge of the sphere is...
  19. N

    Electric Field of a Point Charge

    [moderators note: moved from technical forum, so no template] Summary: I can't tell where the mistake in my process is. The computer keeps telling me I am wrong. The Question: What is the electric field at point 1 in the figure? Give your answer in component form.(Figure 1)Assume that a =...
  20. jisbon

    Finding the launch velocity of a point charge in a e-field

    I'm not sure how to proceed with this, but here are my findings/hypothesis: First we find the electric field contributed by the plate with ##E=\frac{\lambda}{2\pi r\epsilon_{0}}## where r=2? After finding out the electric field, is it safe to assume I can find the acceleration of the point...
  21. jisbon

    Find the velocity of a point charge in a ring of electric field

    Okay, I am not even sure how to startr with this question. But here's my theory: First I will need to the electric field produced by the ring using the formula: ##E = k\frac{\lambda a}{(x^2+a^2)^{3/2}}## After finding out electric field produced by ring, am I supposed to find out the...
  22. K

    Minimum work required to move a point charge

    This is the figure for the problem: 1.) Solved for initial total EPE of the system EPE system = (kq2q3/a) + (kq2q1/b) + (kq1q3/√a^2 + b^2) 2.) Solved for final EPE of the system negating q1 as if it were off to infinity EPE system final = (kq2q3/a) 3.) Plugged values into equation W =...
  23. migueldbg

    Potential from point charge at distance ##l## from conducting sphere

    After looking around a bit, I found that, considering the polar axis to be along the direction of the point charge as suggested by the exercise, the following Legendre polynomial expansion is true: $$\begin{equation}\frac{1}{|\mathbf{r} - \mathbf{r'}|} = \sum_{n=0}^\infty...
  24. R

    A dielectric plate and a point charge: the problem with series

    The problem of the interaction of a point charge with a dielectric plate of finite thickness implies the existence of an infinite series of image charges (see http://www.lorentzcenter.nl/lc/web/2011/466/problems/2/Sometani00.pdf). I introduce notations identical to those used in this work. The...
  25. P

    Voltage measurement of a point charge

    If we have a point charge of significant value, would osciloscope measure voltage if we just point the electrodes in two diffrent point in space?
  26. A

    What is the electric field of a point charge?

    Assuming the point charge lies at the origin, what is the electric field at the origin? Zero or undefined?
  27. Q

    Maximum Horizontal Force of Relativistic Point Charge

    Homework Statement A charge q1 is at rest at the origin, and a charge q2 moves with speed βc in the x-direction, along the line z = b. For what angle θ shown in the figure will the horizontal component of the force on q1 be maximum? What is θ in the β ≈ 1 and β ≈ 0 limits? (see image) Homework...
  28. L

    Flux Through a Cube's Face with our Point Charge at a Corner

    Homework Statement A charge q is placed at one corner of a cube. What is the value of the flux of the charge's electric field through one of its faces? Homework Equations The flux surface integral of an electric field is equal to the value of the charge enclosed divided by the epsilon_naught...
  29. Zack K

    Distance of a Point Charge: Solving for Initial Distance Using Relativity

    Homework Statement You make repeated measurements of the electric field ##\vec E## due to a distant charge, and you find it is constant in magnitude and direction. At time ##t=0## your partner moves the charge. The electric field doesn't change for a while, but at time ##t=24## ns you observe a...
  30. G

    Potential generated by a point charge in a isotropic medium

    Homework Statement When a point charge is positioned at the origin = 0 in an isotropic material, a separation of charge occurs around it, the Coulomb field of the point charge is screened, and the electrostatic potential takes the form \phi(r) = \frac{A}{r} \exp\left( -\frac{r}{\lambda}...
  31. SebastianRM

    What happens to the Electrical Potential the closer we are to a point charge?

    So I have been wondering: The potential for a point charge at the origin, is described as: (Using the reference point at infinity): V=1/(4πε) * q/r My question is, what happens to this Potential the closer we are to the point charge, and so the closer we would get, the Potential seems to go...
  32. B

    Divergence of the E field at a theoretical Point Charge

    I've been thinking about this problem and would like some clarification regarding the value of the divergence at a theoretical point charge. My logic so far: Because the integral over all space(in spherical coordinates) around the point charge is finite(4pi), then the divergence at r=0 must be...
  33. L

    Express E due to a point charge at the origin

    Homework Statement Express the electric field E due to a point charge q at the origin in cylindrical polar coordinates. Homework EquationsThe Attempt at a Solution Know that E = q / 4*pi*epsilon_0*r^2 in the r-direction, which is the answer in spherical coordinates. How we we swap to cylindrical?
  34. J

    Point charge - Assertion & Reason type problem

    Homework Statement Homework EquationsThe Attempt at a Solution These AR type problems are mostly tricky and debatable . To me, A is correct and R is wrong . Although electron is approximated to be a point particle , but I think if R is true , then A will be wrong . I think c) is correct ...
  35. A

    Finding the New Acceleration Given Point Charges

    Homework Statement A point charge q1=15.00μC is held fixed in space. From a horizontal distance of 8.00 cm , a small sphere with mass 4.00×10−3kg and charge q2=+2.00μC is fired toward the fixed charge with an initial speed of 40.0 m/s . Gravity can be neglected. What is the acceleration of the...
  36. Sunanda

    Electric Potential due to a single point charge

    Please refer to the image attached. So, my doubt is: While calculating dW in the derivation, we know this work is being done by external force, because only then the unit positive charge can be made to move towards the charge +Q. So dW should be equal to Fext.dx but here in the book it is shown...
  37. A

    How close will body approach fixed point charge?

    Homework Statement Charged sphere with a mass of 15 mg and charge 2 nC moves with a speed of 15 cm/s towards a fixed point charge of 3 nC. How close will sphere approach charge? Homework Equations K=(1/2)*mv2 U=k*(Q1Q2/r) The Attempt at a Solution So I am not sure I approached correctly but...
  38. A

    Find the amount of work to move a particle from point A to B

    Homework Statement How much work should be done on a point charge of q=15 nC to bring it from infinity to a distance of 3 cm from a surface of a charged sphere? Diameter of sphere is 15 cm, its surface charge density is 12 microC/cm2 Homework Equations W=deltaU=q*deltaV v=kQ/r...
  39. T

    Electric flux of a cube due to a point charge

    Homework Statement Homework Equations Gauss's Law The Attempt at a Solution I simply used logic and observed the symmetry of the cube. If the charge is placed on the middle of the cube, the flux would simply be Q/∈0. The face of the cube itself can be split into 4 squares, with the charge at...
  40. A

    Equivalent point charge, dipole, and quadrupole

    There is a big sphere with charges distributed on the surface. N charges are distributed on a patch of the sphere (all the information of the charges such as their locations are known). Suppose the rest of the sphere has similar charge distribution as the patch, how to approximately calculate...
  41. lightest

    Point charge with grounded conducting planes angled 120

    Homework Statement The problem states: "A point charge q is located at a fixed point P on the internal angle bisector of a 120 degree dihedral angle between two grounded conducting planes. Find the electric potential along the bisector." Homework Equations ΔV = 0 with Dirichlet boundary...
  42. Altair Tans

    Exploring a Universe with One Point Charge

    What if there is a universe with just one point charge in existence....just a charge with vast emptiness around it....now here all laws of physics remain same... But is the concept of field and energy defined there??
  43. Pushoam

    Point charge outside a grounded conducting sphere

    Homework Statement Homework EquationsThe Attempt at a Solution Option (a), because the potential is 0 on the surface, and potential due to point charge is positive so there must be negative charge on the surface. Since opposite charges attract each other, there is an attractive force...
  44. G

    Difficulty with a Point Charge Particle in Electrodynamics

    Point Particle in Relativity and Electrodynamics: “The Classical Theory of Fields” – by Landau and Lifshitz, in its discussion about classical size of a particle, concludes that:- Thus we come to the conclusion that in classical (non-quantum) ‘relativistic mechanics’, we cannot ascribe finite...
  45. Pushoam

    Flux through an infinite plane due to a point charge

    Homework Statement A point charge q is located a distance d meters from an infinite plane. Determine the electric flux through the plane due to the point charge. [/B] Homework EquationsThe Attempt at a Solution I consider another infinite plane at a distance d in the opposite direction. Now I...
  46. Pushoam

    Flux of a point charge through a circle

    Homework Statement Homework EquationsThe Attempt at a Solution I will try to choose the correct option using the common sense instead of solving it. As d decreases, the flux should increase. For R>>d, only option (a) and (d) satisfy this condition. Now, for choosing between (a) and (d)...
  47. Physiker98

    Voltage of thundercloud as point charge

    Hey, Theory: The voltage of a thundercloud is too low to ionize air particles and to produce a thunder. Particles of cosmic radiation are the trigger. I calculated whether the voltage of a thundercloud is enough to ionize air particles but the voltage was always to low. So I wanted to know...
  48. C

    Oscillation of a point charge perpendicular to field lines

    Homework Statement Two particles A and B each carry a charge Q and are separated by a fixed distance D. A particle c with charge q and mass m is kept at the midpoint of A and B. If C is displaced perpendicular to AB by a distance x where x<<<D, find the time period of the oscillation of the...