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
Determine the electric force exerted on a negative point charge –Q located a distance d away from a line segment of charge, extending from –L/2 to +L/2 along the x-axis. The line segment has a non-uniform charge distribution, lambda(x)=lambda_0*x .
Homework Equations...
Homework Statement
There are two point charges aligned on the X-axis. Charge A is a distance -d/2 from the origin and Charge B is a distance d/2 from the origin. What is the potential at a distance z above the center of the charge distribution?
To further clarify
Charge A location at...
Homework Statement
A point charge Q is on the axis of a short cylinder at its center. The diameter of the cylinder is equal to its length L (see figure). What is the total flux through the curved sides of the cylinder? [Hint First calculate the flux through the ends.
Homework Equations...
Electric potential is the work done in moving a unit charge from infinity to a point in an electric field.
Electric potential due to point charge:
V=-\int \vec{E}\cdot d\vec{s}
V=-\int E\cdot ds cos \vartheta
if the stationary charge is positive and
if the test charge is is moved from...
Homework Statement
A point charge q1 = -7 μC is located at the center of a thick conducting shell of inner radius a = 2.6 cm and outer radius b = 4.9 cm, The conducting shell has a net charge of q2 = 1.1 μC.
What is Ex(P), the value of the x-component of the electric field at point P...
http://www.monmsci.net/~fasano/phys2/Chap22_10.pdf
The question is on this PDF File. It's 22.8. I get the logic of it, the electric fields will be 0 only when they both have the same magnitude. The math is shown below the problem, but i don't understand it. Could someone solve this and show me...
I'm trying to find the electric potential inside a thin (not charged) spheric conductor of radius R, containing a point charge of charge +q exactly in the center.
To do this, I'm trying to solve the differential equation \Delta V = 0 (harmonic). Together with the boundary condition V(R) = c...
Homework Statement
We have a metal conducting torus and a point charge that is located on the torus' axis (location on the axis is arbitrary). Calculate the (influenced) charge distribution on the torus and the electrostatic force on the point charge.
Homework Equations
Equation for...
Hi everyone, I took a look at previous questions similar to this one and it seems like I am doing everything correctly, but I still get the wrong answer. Any advice to where I am going wrong would be greatly appreciated!Homework Statement
A point charge (m=1.0g) at the end of an insulating...
My questions are what the book said after working out the solution that I have no issue of finding. The original question is to find E and B at a field point pointed by r due to a moving point charge pointed by w(t_r) at retard time moving at a constant velocity v.
For constant velocity...
The electric field at a point P pointed by the position vector \vec r \;\hbox {, from a moving point charge pointed by a position vector }\;\vec w(t_r)\; at the retarded time is given by:
\vec E_{(\vec r,t)} = \frac q {4\pi\epsilon_0}\frac{\eta}{(\vec{\eta}\cdot \vec u)^3}[(c^2-v^2)\vec u +...
Homework Statement
Use V=kq/r, E(x) = V/x, E(y) = V/y, E(z) = V/z to derive an expression for the electric field at a point charge q.
E(r) = ?
Homework Equations
E= F/Q
Homework Statement
Use V=kq/r, E(x) = V/x, E(y) = V/y, E(z) = V/z to derive an expression for the electric field at a point charge q.
E(r) = ?
Homework Equations
E = F/Q
Homework Statement
what is the magnitude or a point charge whose electric field 50cm away has the magnitude 2nc?
Homework Equations
E=1/4pi.epsilon sub zero q absolute/r sqrt2
1/4pi.epsilon sub zero=8.99x10sqrt9
The Attempt at a Solution
that gives me 71.92 and my solution in the...
Homework Statement
Two particles are fixed to an x axis: particle 1 of charge q1= 2.1 * 10^-8 and particle 2 of charge q2= -4.00q1 at x=70 cm. At what coordinate on the axis is the net electric field produced by the particles equal to zero?
Homework Equations
Enet = E1 + E2
E=F/q
F=k...
I have a small electrode (5x5mm) connected to 200V via a 1Meg resistor.
A charged object is passed 1mm away from the electrode to produce a signal of 100mV.
The static capacitance changes from 25fF to 150fF.
How much of the 100nA drawn from the electric field is due to the change in...
1. A rod 16.0 cm long is uniformly charged and has a total charge of -24.0 µC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its center.
2. How is this problem done?
3...
I mainly have problem is in the final step of the derivation, but I am going to list the steps leading to that:
The question is: Find the potentials of a point charge moving with constant velocity.
Relevant equation:
\vec w(t) = \;\hbox { is position of q at time t.}
| \vec r - \vec...
This is part of the problem in the exercise to find charge distribution of a point charge at origin. I know \nabla \cdot \vec E = \frac {\rho}{\epsilon_0}
\rho = \epislon \nabla \cdot \hat r \frac q {4\pi\epsilon_0 r^2} \;\hbox { where } \vec r = \hat x x + \hat y y + \hat z z
\nabla...
I've got a test coming up on this, and got quite a few of the questions on the related homework wrong. Attached is the problem, my solutions, and the book(correct) solution, please try to find what I'm doing wrong, this is driving me nuts.
Homework Statement
Two charges exist along the...
Homework Statement
A charged particle is fixed in place at the origin. A second particle of charge +10^{-6} C is released from rest from very far away (\approx (\infty, 0)). The second particle passes the point (9 m, 0) with a kinetic energy of 1.0 J.
Find the electric potential due to...
1. Three equal positive point charges of magnitude Q = 5.00μ C are located at three corners of a square of edge length d = 7.8 cm. A negative charge -15.00μ C is placed on the fourth corner. At the position of the negative charge, what is the magnitude of the electric field due to the three...
A point charge generates electric field lines that are radially directed from the source in spherical symmetry. Similarly, a line of charge generates electric field lines that are radially directed from the line of charge in cylindrical symmetry.
Is there any way that a time-varying magnetic...
Hey friends, I am stuck up in the derivation of the electric potential energy due to a charge 'Q' at the origin on test charge 'q' at a point p (position vector 'rp'). The derivation is shown below, am just struggling with a minus sign...
Electric Potential Energy at P
= Work done to move...
Hi All,
I want help to solve a problem:
A point charge is placed at a distance 'L' from the surface of an infinite dielectric slab (permittivity: k1 and thickness 'd'). The entire region of space (outside the slab has a permittivity k2).
First, I need to solve for the energy of the system...
Hi All,
I want help to solve a problem:
A point charge is placed at a distance 'L' from the surface of an infinite dielectric slab (permittivity: k1 and thickness 'd'). The entire region of space (outside the slab has a permittivity k2).
First, I need to solve for the energy of the system...
Homework Statement
A point charge q is a distance a > R from the axis of an infinite solenoid (radius R, n turns per unit length, current I). Find the linear momentum and the angular momentum in the fields. (Put q on the x axis, with the solenoid along z; treat the solenoid as a nonconductor...
Homework Statement
Location A is 3.04m to the right of a point charge q.
Location B lies on the same line and is 3.87m to the right of
the charge. The potential difference between the two locations
is VB - VA = 45.0V . What is the magnitude and sign of the
charge?
Homework Equations...
Homework Statement
A right solid conducting cylinder has a total charge of +5.10 mC. Inside the cylinder a charge q = -1.55 mC rests at the center of a hollow sphere as shown in the diagram below. What is the charge on the surface of the hollow sphere?
Homework Equations
The Attempt at a...
Homework Statement
Ok i got the hard parts, a and b. For some reason I'm stuck on part c, the direction of the electric field.
Consider point a which is 70 cm north of a -4.2 µC point charge, and point b which is 76 cm west of the charge...
Homework Statement
You measure an electric field E at a distance x from a point charge. What is the electric flux through a sphere whose center is at that distance and whose radius is less than x from the charge?
Homework Equations
E*dA = (q_enc)/(e_0)
The Attempt at a Solution
I'm...
Homework Statement
a)A charge Q=10nC is placed at the origin, which is the centre of a cube with side lengths a=1cm whose faces are perpendicular to the x,y and z axis. What is the total flux through the box and what is the average of the perpendicular component of the electric field on the...
Homework Statement
Three charges, q1 = +2.10 10-9 C, q2 = -3.09 10-9 C, and q3 = +1.08 10-9 C, are located on the x-axis at x1 = 0, x2 = 10.0 cm and x3 = 20.0 cm. Find the resultant force on q3.
I am unsure of how to even attempt this problem...
Homework Statement
A point charge +Q is surrounded by a spherical shell of inner radius a and outer radius b. The spherical shell has charge density \alphar.
a) What is the electric field for r < a?
b) What is the electric field for a < r < b?
c) What is the electric field for r > b?
d)...
What?
W = \frac{\epsilon_{0}}{2} \int E^2 d \tau = \frac{\epsilon_{0}}{2 \left( 4 \pi \epsilon_{0} \right)^{2}} \int \frac{q^{2}}{r^{4}} r^{2} sin \theta dr d \theta d \phi = \frac{q^{2}}{8 \pi \epsilon_{0}} \int_{0}^{\infty} \frac{1}{r^{2}} dr = \infty
Griffith explains this infinite energy...
Homework Statement
What is the force on the 1.0nC charge in the middle of the figure due to the four other charges?
http://filesmelt.com/dl/question.JPG
Homework Equations
F = K*q1*q2 / r^2
K = 8.99x10^9
The Attempt at a Solution
Initial observation: The symmetry of the...
Homework Statement
See figure attached for problem statement.
Homework Equations
The Attempt at a Solution
I think my main source of confusion is this problem is how the force is acting on the electron.
The picture shows that the electric field is pointing straight up...
Homework Statement
A uniform electric field of magnitude 8.5×105 N/C points in the positive x direction.
Find the change in electric potential energy of a 8.0 \muC
charge as it moves from the origin to the point (6.0 m , 0). Homework Equations
1 N/C = 1 V/m
\DeltaU = q\DeltaV
E =...
A point charge accelerating through space generates an electric field and radiates energy. But how is this influenced if the point charge is moving along the field lines of an external electric field? Specifically how is calculation of radiated energy effected? Would you add the external field...
Homework Statement
A negative point charge of 10 ^(−6 )C is situated in air at the origin of a
rectangular coordinate system. A second negative point charge of 10^(-4) C is
situated on the positive x-axis at a distance of 50 cm from the origin. What is
the force on the second charge...
Homework Statement
I am trying to find the force acting on a charge placed a distance r0 from the center of a spherical cavity of radius a. The entire cavity is immersed in a dielectric material, epsilon2.
Homework Equations
The Attempt at a Solution
Here's my quandary: I can find the...
2 questions:
1. A point charge of 1.84 microC is at the center of a cubical Gaussian surface 55cm on edge. Find \Phi_E through the surface.
So here I was thinking, well the shape doesn't matter so the surface can be a sphere, so I calculated it for a sphere and it was correct (taking the...
Hi, I received this question on my exam today and it stumped me...
Conducting spherical shell of inner radius 0.045m and outer radius 0.18m, which has a net charge of zero.
A charge Q of 5.5x10-5 is placed at the center, find the electric fields at point A (0.03m), point B (0.06m), and...
Homework Statement
A point charge Q is at the boundary plane of two infinite, homogeneous dielectrics
with dielectric constants \epsilon_1 and \epsilon_2. Calculate the electric potential, the electric field and the displacement vector at any point in space.
Homework Equations...
Electric field of an infinite line charge and a point charge!
Homework Statement
An infinite line charge with linear charge density \lambda=2.0\muC/m lies along the y-axis. A point charge of 8.0 \muC is locate at (x,y)=(-1.0m, 2.0m). Find (a) the electric field at (x,y)=(1.0m, 2.0m) (b) Find...
Hello,
I am having trouble in proving the equation of the electric potential near a point charge Q. There are two different ways I can think to go about deriving the equation V=q/(4*Pi*E0*r). The first way is to calculate the change in potential energy of a test charge q0 in coming from...
Point charge 2.0 uC is located at X= 0, X= 0.30m , point charge -2.0uC is located at X= 0 Y= -0.30m . What are (a)the magnitude and (b)direction of the total electric force that these charges exert on a third point charge Q= 5.0 uC at X= 0.40 , Y= 0?
I drew a diagram of what was...
Two point charges are placed on the x-axis as follows: one positive charge, Q1= 3.96nC , is located to the right of the origin at x = 0.195m , and a second positive charge, Q2= 5.05nC , is located to the left of the origin at x = -0.295m .
What is the total force (magnitude and direction)...
Homework Statement
You have point charge a distance "d" above infinite conducting plane held at V = 0. What is the potential when you remove charge to infinity?
Homework Equations
The Attempt at a Solution
I think I incorrectly used Coulomb's law between the charge (+q...
I'm curious. Say you have a solid, positively charged sphere with a uniform charge distribution. Now suppose you place a single, negatively charged electron inside the solid sphere. How will the electron behave? I assume the electrostatic forces exerted on the electron will ultimately tend it...