Charge density Definition and 419 Threads

1. Homework Statement [/b] A static charge distribution produces radial electric field as follows: \stackrel{\rightarrow}{E}=A\frac{e^{-br}}{r}\stackrel{\rightarrow}{e_{r}} A,b are constants,please compute the charge density. Homework Equations \nabla\cdot...

Homework Statement The y-axis carries a uniform linear charge density of -2 nC/m, and there is a 8 nC point charge at the point (3 cm, 0 cm, 0 cm) as well as a -4 nC point charge at the point (-8 cm, 0 cm, 0 cm). What is the electric flux through a closed spherical surface of radius 4 cm...

Homework Statement An infinitely extended cylindrical region of radius a>0 situated in free space contains a volume charge density given by: [ ρ(r)= volume charge density ρo=constant=initial volume charge density radius=a>0 ρ(r)=ρo(1+αr^2); r<=a ] with ρ(r)=0 for r>a Questions...

Why do I have to integrate? Isn't it redundant? Homework Statement The volume charge density inside a solid sphere of radius a is given by ρ=ρnaught*r/a, where ρnaught is a constant. Find the total charge as a function of distance r from the center. Homework Equations Q=ρV The...

Homework Statement 2. The attempt at a solution I have the solution, but it's pretty confusing so I want to see if anyone else can walk me through step by step. The first step is pretty clear...You have to find the acceleration that the proton will experience as it moves towards the...

Homework Statement I have attached the question as a pdf. Homework Equations I'm thinking that we take the line integral of voltage to get electric field. But I'm not sure how to proceed from here. Is the line integral from a to b? Also, how do I get the charge density having found...

Homework Statement given simple circuit with V the voltage connected to a resistor with area A, length d and electrical conductance: b*e^-2x/d after my computations the resistance R=d*(e^2-1)/(2bA) Homework Equations what is the electrical field E in the center of the...

I am taking a lightning class for my atmospheric science masters degree. However its been awhile and I am having trouble with remembering how to do the physics portion of it. I hope someone can help me! Homework Statement I have an electric field...

Homework Statement For your senior project, you are designing a Geiger tube for detecting radiation in the nuclear physics laboratory. This instrument will consist of a long metal cylindrical tube that has a long straight metal wire running down its central axis. The diameter of the wire...

Homework Statement In a particular region of Earth's atmosphere, the electric field above Earth's surface has been measured to be 147 N/C downward at an altitude of 260 m and 165 N/C downward at an altitude of 410 m. Calculate the volume charge density of the atmosphere, assuming it to be...

here I am only considering the charge density of the nucleus, i.e the density of protons. I know that from mass density i have rho = m/v -> v = m / rho I'm not sure what mass to use here. Molecular weight? molar mass? where does avagadros number come into it? then is it simply charge...

Hi, I'm doing MD-simulations in a capacitor-like system: 2 charged electrodes with a dense ionic liquid in between (non-diluted) with periodic boundaries in 2 dimensions (so for the electrodes I get infinite planes (xy) ,charged). I want to get the potential U(z) along the z-axis (witch is...

In a paper by Coombes and Laue...

The concept of volume charge density is an even distribution of charge over a three dimensional area. C/m^3. However, the concept of electrostatic equilibrium says that all of a conductors charge lies on the surface of the conductor. The existence of one seems, to me at least, to render the...

Homework Statement Hi, This is supposed to be simple, so I guess I miss something.. We have charge q at x1=d*cos (w*t), y=0, z=0. and charge -q at x2=-d*cos (w*t), y=0, z=0. I need to do Fourier transform to the charge density. Homework Equations The Fourier transform is ...

Homework Statement A solid metal sphere of radius 'a' is concentric with a hollow metal sphere of inner radius '2a'. The space between the spheres is filled with a dielectric material of relative permittivity 'ε' carrying a uniform static charge density 'ρ0'. The charge density is zero...

Homework Statement A long round dielectric cylinder is polarized so that the vector P = ar, where 'a' is a +ve constant & 'r' is the distance from the axis.find the space density rho` of bound charge as a function of distance r from the axis. Homework Equations Gauss Law. The...

Electric charge is distributed over a disk x^2+Y^2<=4 so that the charge density at (x,y) is o(x,y)= x+y+x^2+y^2 what is the total charge on the disk so I change to polar and get (rcos +rsin +r^2)rdrdtheta and my limits go from 0 to 2pi and 0 to 2 for my answer i got 8 pi I am...

Homework Statement This is not a home work, I actually make this problem up and work on it. I want to verify whether I am correct in the step and I need help to solve the final integration. The question is: Given a plastic circular ring radius = a with line charge density glued on...

I've already posted this question in the advanced physics forum, but I really think it should go here. My apologies for the double posting. Homework Statement If we are given a uniformly charged solid sphere with total charge Q and radius R, then the volume charge density rho is given by...

How do I work out the charge density of Copper Cu, if atomic mass =63.5 Density = 8920 kgm^-3 Assume 1 electron per cu atom.

Hi, I am new to this forum. I have a question on one of the physics problem. a proton is shot with a speed v from the point a in the vicinity of a infinite straight wire carrying a charge density. in term of these variables determine the nearest distance of approach. Homework Equations...

Homework Statement A proton orbits a long charged wire, making 1.60 * 10^6 revolutions per second. The radius of the orbit is 1.60 cm. What is the wire's linear charge density? Homework Equations F=qE F=ma F=(mw^2)/r F=Eklambda/2r=mw^2/r (the radiuses cancel out) The Attempt at...

Homework Statement Consider two coaxial conducting cylinders with radii a and 3a and length L. The region a<r<2a is filled with a material of conductivity σ1, and the region 2a<r<3a has conductivity σ2. (Assume ε1=ε2=εo.) The inner cylinder is held at potential V0 and the outer cylinder at...

Homework Statement a thin rod of length L is set along an X axis. we want to find the electric field at a point P at the origin, a distance "d" from the rod. The linear change density changes with X and it's given by λ=λ0 ((x-d)^3)/d^3 find the electric field at the point P...

Homework Statement [PLAIN]http://img232.imageshack.us/img232/8974/61038710.png The Attempt at a Solution Well \sigma = charge/area But how am I suppose to find the area if I am not even given the dimensions of the plates?

I wanted to ask if someone can clarify for me when one would use the Heaviside function instead of (or in combination with) the Dirac delta function. Thanks in advance

I have a charge density I would like to plot in 3D The data is currently in the format x1 y1 z1 density x2 y2 z2 density etc etc where x,y,z are grid points. Can this kind of data be formatted as an xyz file? I know xyz is normally atom locations (I have no explicit...

Homework Statement There is a beam of electrons in the space starting at x=0 and ending at x=20cm. The cross section of the beam is A.The velocity of the electrons is a function of position x and let it be v(x).Now i need to calculate the volume charge density as a function of x.Homework...

Homework Statement Suppose an electric field E(x,y,z) has the form: E_x = ax, E_y = 0, E_z = 0 where a is a constant. What is the charge density? How do you account for the fact that the field points in a particular direction, when the charge density is uniform? Homework Equations...

Homework Statement A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0x10^6 N/C. What is the minimum surface charge density for producing a spark? Homework Equations int(EdA) = (Qin) / e0 The Attempt at a Solution I imagine the surface as a cylinder with...

Homework Statement An infinite sheet of charge with a surface charge density of +7.8 micro-Coulomb/m2 lies on x-axis (technically in x-z plane). Another infinite sheet of charge with an unknown charge density lies on y-axis (technically in y-z plane). A positive point charge is placed in first...

1. Consider a long charged straight wire that lies fixed and a particle of charge +2e and mass 6.70E-27 kg. When the particle is at a distance 1.61 cm from the wire it has a speed 2.20E+5 m/s, going away from the wire. When it is at a new distance of 4.01 cm, its speed is 4.00E+6 m/s...

Homework Statement Imagine a spherically symmetric charge density p(x) = Cr for r≤a and 0 for r>a (a) determine the electric field E(x) and potential V(r). Notice that V(r) and E(x) are continuous at r=a. (b) Now suppose additional charge is placed uniformly on the surface at r=a, with...

Homework Statement Two long, thin parallel rods, a distance 2b apart, are joined by a semicircular piece of radius b, as shown. Charge of uniform linear density \lambda is deposited along the whole filament. Show that the field E of this charge distribution vanishes at the point C. DO...

Homework Statement a) A charge q1 = q is at r'1 = -Di, and a charge q2 = -3q is at r'2 = Di. Find an expression for the volume charge density p(r). b) An infinitely long wire along the z-axis has a uniform linear charge density \lambda. Find an expression for the volume charge density p(r) in...

Homework Statement With a Taylor series expansion of the well-behaved \rho ({\bf{x'}}) around {\bf{x'}} = {\bf{x}}, one finds the Taylor expansion of the charge density to be, \rho ({\bf{x'}}) = \rho ({\bf{x}}) + {\textstyle{1 \over 6}}{r^2}{\nabla ^2}\rho + ... Homework Equations...

Homework Statement Let's say we have a wire of finite length L with total charge Q evenly spread along the wire so that lambda=Q/L, linear charge density, is constant. The wire is shaped in x-y plane in some well behaved curve y = f(x). Find the surface charge density sigma(x,y). Homework...

Homework Statement A specified charge density sigma(theta)=kcos(theta) is glued on the surface of a spherical shell of radius R. find the resulting potential inside and outside of the sphere. Homework Equations The Attempt at a Solution This is a worked example in Griffiths. The...

Electric potential at point x on the axis of a ring of charge density "eta" Homework Statement A circular disk of radius R and total charge Q has the charge distributed with surface charge density \eta = cr, where c is a constant. Find an expression for the electric potential at distance z on...

Homework Statement 5. Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20 cm. a) If the surface charge density for each plate has a magnitude of 47.0 nCm^-2, what is the magnitude of the electric field intensity in the region between the...

Homework Statement Sphere of radius R, Er=ER(r4/R4) Find the volume charge density (ρr) as a function of r Homework Equations Gauss's law The Attempt at a Solution I get that dQ=4πr2ρrdr, but have no idea how to solve for ρ

Homework Statement Two rods, of lengths l1 and l2, have charges q1 and q2 a)Find the charges per unit length for each rod individually. b)Find the charge per unit length, averaged over both rods. c)Check your result for l1 approaching 0 d)Check your result for l1=l2 Homework...

Homework Statement When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill the room's air with negatively charged ions and produce an electric field in the air as great as 1000 N/C. Consider a bathroom with dimensions 2.3 m x 3.6 m x 1.6 m. Along...

This isn't the normal kind of homework question, I'm more hoping you can help me fill in the missing steps from this example given by our professor in the class notes. The below example is supposed to assist me in solving my homework problem, I understand everything except the answers circled...

Let's say we have a sphere of charge of radius R, volume V, with total charge Q at t=0, so that we can express this as \rho ( 0 ) = Q/V. Now, if we were to "let go" of this clump of charge, the electrons would fly off due to the mutual repulsion. My question is how to model this, ie, how to...

Homework Statement Suppose the electric field in some region is found to be \bf{E} = kr^3 \bf{\hat{r}} , in spherical coordinates, (k is some constant). (a) find the charge density \rho (b) find the total charged contained in a sphere of radius R, centered at the origin. (do it two...

Hi all, A closed cylinder of Length L, with a radius r and a thickness d is filled with m1q1+m2q2 charges. Their respective volume charge densities are \rho1 and \rho2. The volume is surrounded with a neutral solute (n1q1+n2q2=0) with a volume charge density of \rho3. (see picture)...

Homework Statement The figure shows a portion of an infinitely long, concentric cable in cross section. The inner conductor carries a charge of 6 nC/m and the outer conductor is uncharged. (part 5 of 6) What is the surface charge density inside the hollow cylinder? Answer in units...

What is the difference between current density and linear charge density?