Charge density Definition and 419 Threads

Hi everyone! I'm trying to solve the following problem: given the charge densities of carbon nanotubes and graphene, the charge density difference of 2 systems must be found. So I need to unfold in some way the nanotube and compare it charge density with the graphene's one. But how this...

Homework Statement Sorry, the post isn't about a single homework problem but rather something that I keep getting confused on. It's about calculating the electric potential of a spherical shell of uniform charge in two different ways. Homework Equations ##\Delta V=\int_a^b -\vec E\cdot d\vec...

Homework Statement Let’s say I have got a charge density $\rho (x,y,z) = \cfrac{C}{x^2}$ with C a specific constant. I want to know the potential on every point in space. How can I get an expression of the electric potential in terms of position? Homework Equations Gauss law/coulomb's law...

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 [/B] Using Gauss law, Since there has been no mention of which type of charge density we have to find out I assumed it to be surface charge density since Gauss Law is in surface intergration , and I don't think there is any need to doing integration since the options given...

Hi everyone, there's something that I can't comprehend: when a homogeneous is in a conservative and non-uniform in module electric field polarization expression is given by P=ε0χE. Supposing the most general situation there's: divP=ρp where ρp is the polarization charge density in the...

Homework Statement A sphere of radius R carries charge Q. The distribution of the charge inside the sphere, however, is not homogeneous, but decreasing with the distance r from the center, so that ρ(r) = k/r. 1. Find k for given R and Q. 2. Using Gauss’s Law (differential or integral form)...

Homework Statement Homework EquationsThe Attempt at a Solution In the region |z|<1 , E(z) = -dV/dz = 10zk This means there is a variable electric field in the region -1<z<1 .In the +z region it is directed in the +z direction and vica versa . For finding the charge density in the region...

Homework Statement A parallel plate capacitor is made of two flat horizontal conducting plates in a vacuum, each of area A, separated by a small gap. One plate carries a total charge 2Q, the other a total charge −Q. Find the surface charge densities on the four horizontal metal surfaces in...

Homework Statement A semi-infinite (infinite in y and z, bounded in x) slab of charges carries a charge per unit volume ##\rho##. Electric potential due to this slab is a function of horizontal distance, x from the center of the slab. It is linear for ## x \lt -1m## & ## x \gt 1m##, and is...

Homework Statement An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the...

Homework Statement Consider an infinitely long one dimensional conducting wire with a homeogenous charge density ##\lambda##, running along the central axis of an infinitely long cyclindrical glass casing of radius b (glass is a dielectric material). Calculate: a) The displacement vector...

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...

So I am studying Gauss's law and I am a bit confused about something. If I am asked to compute the volume or surface charge density of a solid perfectly conducing sphere with a charge Q and radius r, what is being asked of me? Am I just being asked to compute the volume of a sphere and multiply...

I am trying to formulate the Current Density for a Loop of wire with a diameter,d, current,I, and an cross-sectional Area of the wire ##\pi(d/2)^2##. With spherical coordinates (radial, azimuthal, polar) ##\bar j## = ##\frac{I}{\pi(d/2)^2}*cos \theta *sin \phi \hat x##...

Homework Statement Consider the parallel plate capacitor(no figure). The capacitor plates have a separation distance d in the z-direction. The volume charge density is given by ρ_v. Find v(z).Homework Equations ρ_v = ρ_o*sin(pi*z/2*d) The Attempt at a Solution [/B] ∫(ρ_vdz) =...

Homework Statement Consider a ring of radius R placed on the xy-plane with its center at the origin. A total charge of Q is uniformly distributed on the ring. a) Express the volume charge density of this configuration ρ(s,Φ,z) in cylindrical coordinates. b) Express the volume charge density of...

Homework Statement A point charge ##q = −5.0\times 10^{−12} C## is placed at the center of a spherical conducting shell of inner radius 3.5 cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is...

Homework Statement An infinitely long line of charge has linear charge density ##λ=4.00_{10^{−12}} \frac{C}{m}##. A proton (mass ##m_p=1.67_{10^{-27}}kg##, charge ##e=1.602_{10^{-19}}C##) is ##r_a=0.18m## from the line and moving directly toward the line at ##v=1000\frac{m}{s}##. Homework...

Homework Statement "A straight, nonconducting plastic wire ##x=9.50_{10^{-2}}m## long carries a charge density of ##λ=1.3_{10^{-7}} C/m## distributed uniformly along its length. It is lying on a horizontal tabletop. If the wire is now bent into a circle lying flat on the table, find the...

Homework Statement Homework EquationsThe Attempt at a Solution ##\rho = b r \\E =\frac { k r^2} {4ε_0} \\ p ∝ E^a \\E \left ( r=d \right ) = \frac { k d^2} {4ε_0} \\ p = q d \\ d ∝ d^{2a} \\a = ½ \\p ∝ √E ## PART B ##\rho ∝ r^n \\E ∝r^{n+1} \\ p ∝ E^a \\d ∝d ^{{n+1}a} \\## For eq. 4.1 to...

Currently, I am reading this article which introduces electromagnetism. It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$ The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory...

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 A positively charged nonconducting solid sphere of radius R has a nonuniform volume charge density given by ρ0 for r≤R/2 and given by 2ρ0(1−r/R) for R/2 ≤r≤R, where r is the radial distance from the sphere center.Part A Determine the charge q on the sphere in terms of ρ0 and...

Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...

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 A nonconducting sphere of radius r0 carries a total charge Q. The charge density ρE increases as the square of the distance from the center of the sphere, and ρE=0 at the center. a) Determine the electric potential as a function of the distance r from the center of the...

Homework Statement A uniform spherical charge density of radius R is centred at origin O. A spherical cavity of radius r and centre P is made. OP = D = R-r. If the electric field inside the cavity at position r is E(r), the correct statement is: 1)E is uniform, its magnitude is independent of r...

Hi, Let's think 2 arbitrary shape conductors with non zero charged. If these 2 conductors are closed, there will be induced charge density over surfaces of these conductors. I have not seen such an example, instead there are lots of problems which involve zero(grounded) potential case and...

Homework Statement I'm having a bit of trouble with this problem: "A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r≤R) is E(r)=r^4Emax/R^4. a. What is Emax in terms of Q and R? b. Find an expression for the volume charge density ρ(r)...

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 Homework EquationsThe Attempt at a Solution I don't understand how it looks like, how to approach this problem. I think it's maybe image charge or Laplace equation

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...

Homework Statement Theres a cylinder rod inner radius a outer raidus b.we want to find electric field between a and b,like point r (or radius r) a<r<b. Homework Equations Gauss Law The Attempt at a Solution [/B]I am trying to find Q enclosed but something make me confused.I am...

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 Homework EquationsThe Attempt at a Solution I have the full solution, the first part being: I don't understand how they came up with the expression for Vab. I know usually ΔV=-∫E dl, but I'm not sure how they found their expression. Can someone explain? Thanks.

Homework Statement Insulator has a 3 cm radius and is a sphere. It has a total charge of -4.2 uC. I need to find the charge density of the insulator. Homework Equations sigma = total charge / volume... I think? The Attempt at a Solution After using the above equation, I got -3.714E-8 C/m I...

Homework Statement Calculate the surface charge density induced by a point source above an infinite conducting plane, with 0 potential. Homework Equations ##E=-\nabla V## ##V=\frac{q}{4\pi \epsilon_0 r}## The Attempt at a Solution I used the method of image charges and I calculated the...

Homework Statement Given the electric potential ##V(r)=A\frac{e^{-\lambda r}}{r}## calculate the charge density ##\rho(r)## and the electric field ##E(r)##. They specify the answer for charge density should be: ##\rho = \epsilon_0 A(4\pi \delta^3(r)-\lambda^2e^{-\lambda r}/r)## Homework...

Hello! I am a bit confused about calculating the induced surface charge density on an infinite conducting plane, with 0 potential, in the presence of a charge, q, a distance d above it. Assuming that the plane is in xy plane and the charge in positive z region, in the book they use the method of...

Homework Statement The potential difference between the surface of a 2.2 cm -diameter power line and a point 1.9 m distant is 3.8 kV. What is the magnitude of the line charge density on the power line? Express your answer using two significant figures. Homework Equations V =...

Homework Statement The electric field strength just above one face of a copper penny is 2230 N/C. What is the surface charge density on this face of the penny? Homework Equations Electric field of an infinite plane of charge = η/(2*ε0) The Attempt at a Solution I used the above equation, and...

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 Homework Equations E=σ/(2Eo) σ=2Eoma/e a=Δv/Δt The Attempt at a Solution So doing my best to read the velocity over time graph I came up with Δv/Δt=(-2E5m/s)/(10E-12s)=-2E17 m/s/s σ=2Eoma/e =2(8.99E-9C)(9.109E-31kg)(-2E17m/s/s)/(1.6022E-19) =-0.020444 C/m^2 but by the...

Homework Statement Tasks to do: a.)give voltage b.)give the absolute value of charge density for plates Presumably the absolute values of charge densities for plates is equal between the two of them. An electron is accelerated in a homogenic electric field, inbetween two oppositely charged...

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 Attempt...

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...