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. B

    Electric Flux through a Spherical Surface at the Origin

    Homework Statement A point charge q_1 = 3.45 nC is located on the x-axis at x = 1.90 m, and a second point charge q_2 = -6.95 nC is on the y-axis at y = 1.20 m. What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius...
  2. J

    Calculating Work Required to Move a Point Charge of +8μC from (0,4m) to (3m,0)

    A point charge, Q=+1mC, is fixed at the origin. How much work is required to move a charge, q=+8(micro)C, from the point (0,4meters) to the point (3meters,0)? I was unable to derive anything. I guessed at around 40J. Correct? If so HOW! lol
  3. S

    Lienard Wiechert potential of a point charge ?

    Good day to everybody, I got stuck at certain (basic) question regarding Lienard Wiechert (LW) potential of a point charge: In Heitler's great book "Quantum Theory of Radiation" (I've used the edition from 1954), on page 18, there is a familiar statement that: \frac{e}{r}|_{t-r/c} is not...
  4. J

    Surface charge induced in conductor by point charge

    Homework Statement Find the surface charge induced on an infinite conducting plate by a point charge +q at a distance a from the plate. The Attempt at a Solution As you probably know, this problem can be solved using the well-known fact that the induced electric field is equivalent to...
  5. I

    Potential of a Dielectric sphere and an exterior point charge.

    Consider a sphere of radius a with dielectric constant epsilon. A point charge q lies a distance d from the center of the sphere. Assume d > a, calculate the potential for all points inside the sphere, and outside the sphere. The problem is to be solved with an expansion of Legendre...
  6. S

    Calculate W for Point Charge Configuration

    If you calculate W, the amount of work it took to assemble this charge configuration if the point charges were initially infinitely far apart, you will find that the contribution for each charge is proportional to {kq^2}/{L}. In the space provided, enter the numeric value that multiplies the...
  7. G

    Electric field on point charge

    Homework Statement what is the electric field at point A (0,12) if there is charge c of 8*10^-9 coulombs at (16,0) and a charge d of 6*10^-9 coulombs at (-9,0) determine x and y components of electric field (see diagram) Homework Equations electric field e = kq/r^2 where k is 9*10^9...
  8. S

    Point charge / potential / work

    Homework Statement Two point charges q1 = +2.80 nC and q2 = -6.30 nC are 0.100 m apart. Point A is midway between them and point B is 0.080 m from q1 and 0.060 m from q2 (Fig. 23.29). Take the electric potential to be zero at infinity. ***Figure attached*** (a) Find the potential at...
  9. G

    Point charge attractioning a positive charge from infinity to 30cm

    Homework Statement A point charge of 2.0 10-9 C is located at the origin. How much work is required to bring a positive charge of 4.0 10-9 C from infinity to the location x = 30.0 cm? and it requests the answer in J Homework Equations W=-q2(delta)V DeltaV = Ke q1/d where...
  10. A

    Dielectric Sphere in Field of a Point Charge

    Hi, I have derived the electric potential equations inside and outside the sphere due to a point charge q placed a distance b way from the sphere's center. The potentials are given by: \Phi_{in}(r,\theta) = \sum^{\infty}_{n=0} A_{n}r^{n}P_{n}(cos\theta) and \Phi_{out}(r,\theta) =...
  11. A

    Electric Field of a Point Charge

    Hi, A simple question: Is the electric field of a point charge infinite at the charge itself? Coulomb's Law clearly seems to say so, but I just want to be certain. Thanks
  12. T

    Electric field due to point charge

    Homework Statement Two particles are fixed to an x axis: particle 1 charge -2.00x10^-7 at x=6.0cm and particle 2 at 2.00x10^-7 C at x=21.0cm. Midway between the particles, what is there net electric field? Homework Equations E=kq/r^2 The Attempt at a Solution Ok so I drew the...
  13. R

    Voltage at Halfway Point Between Point Charges in an Equilateral Triangle

    Homework Statement There is an equilateral triangle with one point charge at each vertex. The point charges have charges of +Q, +2Q, and -4Q. The length of one side of the triangle is L. Determine an expression in simplest form for the voltage at a point halfway between the +Q and +2Q point...
  14. K

    Work Done on Proton by +3microC Charge: Find V at 50cm & 35cm

    A proton is moved at a constant velocity towards a stationary +3micro coloumb point charge that cannot move. The proton is initially 50 cm away from the point charge and the proton is moved until it is 35 cm away from the point charge. A) How much work was done on the proton? B) If released...
  15. W

    Solve Point Charge Deflection: Potential Difference Between Plates

    Homework Statement A point charge of mass 0.069 kg and charge q = +5.89 µC is suspended by a thread between the vertical parallel plates of a parallel-plate capacitor. If the angle of deflection is 22°, and the separation between the plates is 0.025 m, what is the potential difference...
  16. N

    Finding the electric potential of point charge

    [SOLVED] Finding the electric potential of point charge Homework Statement I want to find the electric potential at a distance r from a point charge. Here's what I'm doing: We have V = - \int {E \cdot {\rm{d}}{\bf{l}}} I find that V = - \int_\infty ^r {k_e \frac{q}{{r'^2 }}{\bf{r}}...
  17. S

    Capacitance of point charge electrode

    Consider a capacitor which is just like a plate capacitor, but instead of the upper electrode being a plate it is a point charge Q. the lower plate is held at a fixed potential V=0. how could you calculate the capacitance of the system? when trying to calculate - it looks like it will be 0...
  18. D

    Is the Energy of a Point Charge Finite or Infinite?

    Hi, I read in the Feynman Lectures Vol II that the assumption that the electron is a point leads to an infinite energy in its field, and that the difficulty hasn't been resolved. Has there been any progress on this since Feynman gave his lectures?
  19. L

    Shileding of a point charge by an infinite conducting plane

    Hi everyone, I have some queries regarding the situation where a point charge is placed at a distance from an infinite conducting plane:say the plane is the xy plane and the charge is above it at distance z: 1) If the plane is at non-zero potential, is that true that the plane will not...
  20. S

    Force induced on a point charge by two conducting planes

    Homework Statement A point charge q is located in the xy plane near two grounded conducting planes intersecting at right angles as shown in the Figure. The z axis lies along the line of intersection of the planes. Find and justify (mathematically show) the force acting on this charge q...
  21. B

    Find the magnitude and sign of the point charge at the origin

    Homework Statement The value of the Electric field at a distance of 82.8 m from a point charge is 75.3 N/C. Its direction is radially in toward the charge. The Coulomb constant is 8.98755 E9. Find the magnitude and sign of the point charge at the origin. Answer in units C. Homework...
  22. I

    Calculatin units for theoretical magnetic point charge

    Hi, So, assuming the theoretical existence of a monopole, we would have to alter the maxwell equations to give the magnetic field a divergence, and also to ensure that the divergence of the curl of the electric field is still zero we would have to add a term. The altered divergence of B would...
  23. J

    Hi and point charge vector question

    Hi all this is my first post. This looks like a great forum and hopefully I can contribute in some way to the discussion. I have a question about JPEG I attached; hopefully you all can see it. What is the strategy for "reducing the charges"? For instance, why is -3q reduced to -2q and...
  24. A

    Calculating Energy, Force, and Torque of a Dipole in a Point Charge Field

    Homework Statement A dipole sits a distance d above a point charge q which is located at the origin of our coordinate system. In (a) it is aligned in the z direction and in (b) in the y direction. Calculate the energy, force, and torque of the dipole in the field of the charge. (see...
  25. B

    Calculating the Kinetic Energy of a Point Charge From Far Away

    Homework Statement Four point charges form a square with sides of length d. Use k as the constant instead of 1/4*pi*epsilon not. +q_______-3q +2q______+5q What would be the kinetic energy for 2q at a very large distance from the other...
  26. rocomath

    Point charge formula and set-up

    I just have a general question. Coulomb's Law is ... F=\frac{k\cdot |q_1||q_2|}{r^2} Ok, solving this question ... Three point charges are arranged along the x-axis. Charge q_1=+3.00\mu C is at the origin, and charge q_2=-5.00\mu C is at 0.200 m. Charge q_3=-8.00\mu C. Where is q_3...
  27. Z

    Electric field and point charge problem

    Homework Statement A particle with mass m and chare, q<0, moves in the field of a POINT charge Q>0, which is fixed in the origine of a cartesian coordinate system. The particle starts at REST in a distance R on the x-axis of a cartesian coordinate system : r(o)(vector) = Rix(vector), V(o)...
  28. J

    Point charge and a plane question

    OK I'm really not understanding any of this, please help, and any tips on how to go about problems like this in general would be much appreciated. Homework Statement A point charge Q is situated a distance d from an infinite conducting plate connected to ground. Show that the total charge...
  29. S

    Point charge at the center of a spherical conductor

    I have the problem A positive point charge of magnitude 2.4 micro Coulombs is at the center of an uncharged spherical conducting shell of inner radius 65 cm and outer radius 85 cm. I have been trying to calculate the total charge for the inner sphere. I solved for the Electric Field by...
  30. A

    Electric field due to two point charge

    Two point charges are placed on the x axis. The first charge, q1 = 8.00nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.0nC , is placed a distance 9.00m from the origin along the negative x axis. Find the electric field at the origin...
  31. H

    Electric Field Vector for point charge

    b]1. Homework Statement [/b] Point charge q1= -5.00 is at the origin and point charge q2= +3.00 is on the -x axis at x= 3.00 cm. Point P is on the y-axis at y= 4.00 cm . Calculate the electric fields E1 and E2 at point P due to the charges q1 and q2. Express your results in terms of...
  32. A

    Point Charge Problem: Net Force Calculation

    Homework Statement Two Positive charges q1 = q2= 2.0 microC are located at x=0, y = .30 m and x =0, y =-.30m. Third point charge Q =4.0 microC is located at x=.40 m, y = 0. What is the net force magnitude and the direction on charge q1 exerted by the other two charges. Homework Equations...
  33. B

    Finding the Mirror Image Charge for a Point Charge Near a Conducting Sphere

    Homework Statement A point Charge Q is placed a distance R from the center of a conducting sphere of radius a, with R>a, i.e. the point charge is outside the sphere. The sphere is grounded- connected to a distant, unlimited source/sink of charge at zero potential. (Neither the distant...
  34. J

    Stationary point charge in increasing magnetic field

    hi everyone, if a stationary point charge is placed in an increasing magnetic field, is the force on the charge due to the magnetic field = 0? because Fb = qv*B and v=0 then how would I derive the magnitude of the force on the charge due to the magnetic field with the magnetic field...
  35. U

    Point charge and electric potential

    Homework Statement three point charges, each of 10^-9 are located at 3 corners of a square of side 20cm. Calculate the electric potential at the forth corner. Homework Equations V = Q / (4(pi)(epsilon 0) r) The Attempt at a Solution Potential because of corner A = 10^-9 / (4...
  36. S

    Electric Flux through an Infinite Plane due to a Point charge

    Homework Statement A point charge of 43 microcoulombs is located a distance 48 meters from an infinite plane. Determine the electric flux through the plane due to the point charge. Homework Equations flux = integral E d A = enclosed charge / epsilon_0 E = kQ / r^2 The Attempt at a...
  37. G

    Electric field of a line charge and point charge

    A thin rod 39.2 cm long is charged uniformly with a positive charge density of 72.0 mC/m. The rod is placed along the y-axis and is centered at the origin. A charge of +46.5 mC is placed 68.4 cm from the midpoint of the rod on the positive x-axis. Calculate the electric field at a point on the...
  38. H

    Zero divergence in an enclosed point charge

    Why does an enclosed point charge have zero divergence/flux? Mathematically I can see that when the divergence operator is applied to E=q/r^2 (pointing in the r direction) I get zero, but what is the physical explanation for what is going on? I am confused because other enclosed electric fields...
  39. S

    Potential due to point charge

    Homework Statement The electric potential at a distance of 20.5 cm from a very small charged sphere is 33.0 V, with the potential taken to be zero at an infinite distance from the sphere. If the sphere is treated as a point charge, what is its charge? Homework Equations V = \frac {U}...
  40. Y

    Calculating Point Charge Potential at (0,0,0)

    Hallo! Homework Statement Consider electrostatic Potential of point charge at point (0,0,0) \phi = 1/r I'm trying to calculate \Delta\phi Homework Equations The Attempt at a Solution Actually it's not a difficult problem outside (0,0,0): \nabla\phi = -\frac{\vec r}{r^3} \Delta\phi = 0 But...
  41. D

    Electric Potential Produced by Point Charge

    Homework Statement A point charge of -8 µC is at the origin. What is the electric potential at (a) (3.0m, 0), (b) (-3.0m, 0), and (c) (3.0m, -3.0m)? Homework Equations V=kq/r The Attempt at a Solution a & b) V=(8.99x10^9)(-8x10^-6)/3 V= -23973.3 c)...
  42. S

    What is the force on a point charge in Griffiths problem 8.4?

    Griffiths problem 8.4 1. Homework Statement Consider 2 eual point charges q, separated by a distance 2a. Construct the plance equidistnace form the two charges. By integrating Maxwell's stress tensor over the plane determine the force of one charge on the other. Homework Equations...
  43. D

    Find Electric Flux through cube's side, point charge on corner

    My problem is this, Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. I am thinking I need a double integral. One to swipe the box in the y direction...
  44. M

    Point charge between two conducting plates

    Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate. I solved this problem assuming (intuitively) that a potential difference between plate 1 and 2 equals 0 and...
  45. B

    QED vs Point Charge of the Electron

    If the electron is a point charge, then its' charge to mass ratio approaches infinity. How does the Standard Model (QED) deal with this?
  46. maverick280857

    Point charge placed in the vicinity of two plates

    Hello all.. Here's a question I need some help with... A point charge +Q has been placed between two infinitely large conducting plates. The charge induced on the surface of the first plate is q_{1}. What should be the charge induced on the surface of the second? (Diagram attached; the...
  47. P

    Electric fields and positive point charge

    A positive point charge q is placed at x=a and a negative point charge -q is placed at x=-a. a: find the magnitude of the electric field and the direction at x= 0. b: derive an expression for the electric field at points on the x-axis. use results to graph the x-component of the electric field...
  48. M

    Find the force on a point charge

    A charge is spread uniformly along the y-axis from y=0 to y=∞. The charge density on the y-axis is λ. Find the force on a point charge q placed on the x-axis at x=x0
  49. S

    Understanding Point Charges: Same Sign, Different Magnitudes?

    Please Help! I would really appreciate some help on this one...I'm pretty sure I'm making it harder than it is... The question is this - "Three point charges are fixed to the corners of a square, one to a corner, in such a way that the net electric field at the empty corner is zero. Do...
  50. M

    What is the total energy of the point charge?

    I need help with this question. I can't see the motion. I have Consider a solid sphere of radius R with a charge Q distributed uniformly. Suppose that a point charge 'q' of mass 'm', with a sign opposite that of Q, is free to move within the solid sphere. Charge q is placed at rest on the...
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