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.
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...
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
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...
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...
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...
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...
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...
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...
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...
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) =...
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
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...
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...
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...
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...
[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}}...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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}...
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...
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)...
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...
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...
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...
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...
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...
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
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...
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...