A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round...
Hi everyone, this is my first thread!
I am currently undergoing a personal investigation that is based on one of the factors which effect the splitting of d orbitals in central metal ion by the charge density of ligands (in a complex ion).
However, recently I got stumped by trying to...
Homework Statement
Consider a charged body of finite size, (\rho=0 outside a bounded region V). \vec{E} is the electric field produced by the body. Suppose \vec{E} \rightarrow 0 at infinity. Show that the total self-force is zero: \int_V \rho \vec{E} dV = \vec{0}, i.e. the charged body does not...
Homework Statement
A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere?
Homework Equations
Charge density ρ=dQ/dV
Gauss's Law ∫EdA = E(4ϖr^2)
The Attempt at a Solution
If Q is uniform then ρ=Q/dV and the...
Homework Statement
Distance between plates of a parallel-plate vacuum capacitor is d. The capacitor is attached to a battery that keeps it at a voltage V. The space between plates is now filled dielectric relative permittivity epsilon. How will charge density of the plates change?
Homework...
Homework Statement
With regards to a one dimensional conducting wire with a homogeneous charge density λ surrounded by a cylindrical glass dielectric of radius R, find:
(a). The displacement vector inside the dielectric
(b). The surface bound charges on the surface of the dielectric
Sorry...
Homework Statement
A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R).
This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere.
a. Show that ρ_0 = 3Q/πR^3.
b. Show that the electric field inside...
Homework Statement
(i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate.
(a) Find the electric field inside and outside of the sphere
(b) Find and plot the electric potential inside and outside of the sphere...
Homework Statement
Given an electric field $$\vec E(x,y,z)=\begin{pmatrix}ax^2+bz\\cy\\bx\end{pmatrix},$$with nonzero constants ##a,b,c##, I am supposed to find the charge density ##\rho(x,y,z)## which is necessary to create this field ##\vec E##.
Homework Equations
##\rho=\frac{\mathrm...
Homework Statement
In an abrupt p-n junction we consider the junction between one side p-doped with ##N_A## acceptor atoms and another side n-doped with ##N_D## donor atoms. Initially the chemical potential is different in the two sides, but thermal equilibrium requires that the chemical...
I'm working on this: When I consider a disc with radius ##a## and total charge ##Q## uniformly distributed (placed in the XY plane and centered at the origin) and determine the volume charge density in cylindrical coordinates, I have assumed is of the form ##\rho=A \delta (z) U(R-r)##, (##U## is...
Homework Statement
Two 10-cm-diameter metal disks separated by a 0.64-mm-thick piece of Pyrex glass are charged to a potential difference of 1100 V .
What is the surface charge density on the disks?
What is the surface charge density on the glass?
Homework Equations
C=(e_0A)/d
C=Q/V
charge...
Homework Statement
##e_{r1}=2##
##e_{r2}=10##
##α_1=\pi /4##
##D_1=100 nC/m^2##
##ρ_s=0##
On the borderline of two dielectrics there is no free charge. Calculate the surface bond charge density of both dielectrics.
##ρ_{bs1}=?##
##ρ_{bd2}=?##
Homework Equations
3. The Attempt at a Solution...
Homework Statement
[/B]
Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space.
Homework Equations
3. The Attempt at a Solution...
Homework Statement
A very thin plane of length ##2a## is placed in the air at height ##a## above the conducting surface. The plane is charged on its surface and the expression for it's surface charge density (##ρ_s##) is given by ##ρ_s=ρ_{s0}*\frac{x}{a}## and ##ρ_{s0}## is some constant.
a)...
1. Homework Statement :
Homework Equations :[/B] A conductor is an equipotential surface. The charge density near a conductor is proportional to the electric field. Electric field is the negative gradient of potential and thus electric field is in a direction normal to the surface.
The...
Homework Statement
Lets say you have a infinitely long surface with one side of length ##L## and a surface charge density ##ρ_s## and you need to transform that into a linear charge density ##Q'## so that you can represent the surface along some axis ##y## so the the surface is placed normal to...
Hi.
Is the Maxwell equation
$$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$
even true in the stronger form
$$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$
I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...
Why must steady currents be non-divergent in magnetostatics?
Based on an article by Kirk T. McDonald (http://www.physics.princeton.edu/~mcdonald/examples/current.pdf), it appears that the answer is that by extrapolating the linear time dependence of the charge density from a constant divergence...
1. Homework Statement
Calculate the resultant electric field acting on some point ##x##. The electric field is generated by a long thin rod and the line charge density is given. ##p_l=\frac{dQ}{dL}##
Homework Equations
3. The Attempt at a Solution [/B]
I have uploaded two images, one of the...
As the name of the thread says, I am wondering what would the amount and the direction of the electric field at some point in the uniformly charged ball of radius R(it has a constant charge volume density) be at the distance r from the centre of the ball. Does anyone know what would they be? I...
Homework Statement
A thin rod of length 2ℓ has a linear charge density that is λ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero.
What is the magnitude of the electric field along the rod's axis at a...
Homework Statement
I am trying to solve Problem 2.45 in Electrodynamics by Griffiths, however, my answers were different from those in the book, I am suspect I got a missing step but I could not find it, so here is the Given Problem
Find the charge density \rho given by a potential...
Suppose I want to collect 1 esu (2.081 billion charges) on a plate or on a ball, what is the smallest radius that will carry such a charge?
From data I gathered around a ball of 1 mm of radius would be large enough, can you confirm that? What material is best, steel, silver or non-conductive...
Homework Statement
Find potential and charge per unit length of every cylindrical hollow shell if the outer shell is grounded. The length is considered to be infinite.
Homework Equations
V=∫Edl
The Attempt at a Solution
I am not sure how to derive potentials for first two conductors...
Homework Statement
Homework Equations
E= kq/(r^2), E*dA = Q/e0
The Attempt at a Solution
Typically I understand how to interpret basic graphs such as going for V (potential) vs x graph to Electric field vs x graph by finding the slope of V since E= -grad V...and from their it's basic...
1. A charge density ρ (charge per unit volume) is distributed uniformly throughout a non-conducting cylinder of radius R. What is the magnitude of the electric field a distance r = R/2 from the cylinder's axis?
Homework Equations
E ∫dA = q(interior)/ε0[/B]
3.
So I tried doing EA =...
Homework Statement
Consider a nonconducting sphere of radius r2. It has a concentric spherical cavity of r1. The material between r1 and r2 has a charge density p (C/m3). Take V=0 and r=infinity. Determine the electrical potential V as a function of the distance r from the center for (a) r>r2...