Charge density Definition and 439 Threads

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 Write an equation in vector component form for the force when a point charge q0 is located a distance d from a vertical rod of uniform charge density Q and length L on the 45o line that bisects the positive x and y axes. basically if you can picture a rod going vertically...

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?

Homework Statement A large plane having uniform charge density has an electric field just outside the plane that points directly toward the plane with magnitude 1.50×10^4 N/C . What is the surface charge density? Express your answer with the appropriate unit Homework Equations I am...

Homework Statement Consider a model semiconductor with a bandgap of 1.0 eV which is doped with 10^17 /cm^3 acceptors for x<0 and 10^17 /cm^3 donors for x>0. E_c - mu = 0.1 eV on the far left and on the far right (far from x=0) Homework Equations The Attempt at a Solution...

Homework Statement "Consider a charge density distribution in space given by [rho] = [rho]_0 * e^(-r/a), where [rho]_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r. Sketch the E vs. r graph. Was a question on a quiz...

Homework Statement If the Earth's surface was charged to QTOTAL = 13548.3 [C] by removing all of the electrons from a volume of soil, how large would this volume be? Assume electron density of soil = 7e23 [cm-3]. Homework Equations Volumetric charge density pv = QTOTAL/volume of soil...

Homework Statement A point charge, Q, is located @ (0,0,d) above infinite conducting plane that lies in xy plane and is maintained at ground potential. Find: a.) surface charge density as a function of x and y on conducting plane, and b.) total charge induced on conducting plane...

Homework Statement You are informed that the charge density is: $\rho \left( r \right)=k{{r}^{-n}},r<a$, where k is a constant and n is a whole number. Determine n. Homework Equations Besides that, I know that: \[E=\frac{Q}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{r}^{2}}},r<a\] (E is...

1. A spark occurs at the tip of a metal needle if the electric field strength exceeds 4.00×106 N/C, the field strength at which air breaks down. What is the minimum surface charge density for producing a spark? 2. surface charge density = Q/A 3. The answer is 3.54*10-5 C/m2. How was this...

Homework Statement A sphere with excess charge of 1.5 x10 -7 Coulombs, An outer radius of 2.5cm and inner radius of 1.5 cm ( a cavity ). The question is to find the surface charge density on the inside surface. I'm totally at a loss on this one and couldn't find how to solve it...

Homework Statement The electric field produced by a static electric charge Pe(R) at a point R in free space is give by, E(R) = (R3+AR2) R\hat{} , R<a E(R) = B(a5+Aa4)R-2 R\hat{}, R>a Where a, A and B are arbitrary constants and R spherical coordinate system radial vector (R locates...

Homework Statement a 5 cm radius conducting sphere has a charge density of 2x10^-6 C/m^2 on its surface. Its electric potential, relative to the potential far away is? Homework Equations I used V= K(q/r) The Attempt at a Solution Using the above equation I got 1.12 x 10^4. This...

Homework Statement In the atmosphere and at an altitude of 250 m, you measure the electric field to be 150 N/C directed downward, and you measure the electric field to be 170N/C directed downward at an altitude of 400 m. Calculate the volume charge density of the atmosphere in the region...

A small, nonconducting ball of mass 1.4E-6 kg and charge 1.9E-8 C hangs from an insulating thread that makes an angle of 32 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and...

Homework Statement An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.60 mm. 1. If a 25.0 V potential difference is applied to these plates, calculate the electric field between the plates. 2. What is the surface charge density...

Homework Statement An infinite cylinder of radius \textbf{R} has a linear charge density \lambda. The volume charge density \frac{C}{m^{3}} within the cylinder (r\leq R) is \rho(r)=\frac{r\rho_{0}}{R} where \rho_{0} is a contant to be determined. The charge within a small volume...

Homework Statement A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find: (a) the charge density of each face of the plate and (b) the total charge on each face Homework...

Is my procedure/result correct? Are these equations relevant for the problem? Many thanks! Homework Statement - blue color on the picture Homework Equations - black color on the picture The Attempt at a Solution - black color on the picture...

Homework Statement We know that free charges inside a conductor will eventually move to the conductor surface. Consider a free charge initially placed inside a conductor at t=0. Show that the free charge density \rho_f will dissolve exponentially with time. Express the characteristic time...

Homework Statement Center a rod of length L at (0,0) with the length going horizontally. Take a point P at (0,y). Find the electric field at P. Homework Equations \lambda=Q/L E= \int k*dQ/R^{2} The Attempt at a Solution I am integrating from -L/2 to L/2 Since Q=lambda*L, I...

This is actually a problem in my Vector Calc class, but is very fitting for this section. I have been trying to understand this problem, and cannot seem to figure out where to go. The z-axis carries a constant electric charge density of λ units of charge per unit length with λ > 0. The...

Homework Statement A sphere of radius R, centered at the origin, carries charge density ρ(r,θ) = (kR/r2)(R - 2r)sinθ, where k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere. Homework Equations...

Homework Statement i have: a nonconducting sphere of radius 25 cm. the electric field points radially away from the center of the sphere, and increase linearly from 0 to 3700V/m at the surface of the sphere. determine charge density? Homework Equations i think the E=E0+r*148 The Attempt at a...

Calculate the dipole moment of a spherical shell of radius 'a' whose surface charge density is σ=σ0(1+cos(θ)). The origin is at the center of the sphere. What I know: 1) p=∫r'*ρ*dV' I'm having trouble understanding how to transform this equation so that I can calculate the dipole moment...

Homework Statement What is the electric field inside a a solid of uniform chage density i.e. \mathbf{E}(\mathbf{r})=\frac{1}{4\pi\varepsilon_0}\int_V\rho(\mathbf{r}')\frac{\mathbf{r}-\mathbf{r}'}{|\mathbf{r}-\mathbf{r}'|}dV' What is the electric field at \mathbf{r}'=\mathbf{r} if...

Homework Statement the volume charge density Pe= Po (1- (r^2/r0^2)) the sphere has a radius of r0 and r is measured from the center for a point P inside the sphere (r<r0), determine the electric potential V if V=0 at infinity Homework Equations E= Qencl/ eps0*A= kQ/r^2 Qencl=...

Homework Statement The surface of a sphere of radius a is charged with a constant surface density \sigma. What is the total charge Q' on the sphere? Find the force produced by this charge distribution on a point charge q located on the z axis for z > a and for z < a.Homework Equations The...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function. Homework Equations The three dimensional charge density is the total charge over a...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function.Homework Equations The three dimensional charge density is the total charge over a volume.The...

Homework Statement A sphere of radius a has a charge density which varies with distance r from the center according to http://img14.imageshack.us/img14/9577/wangsnessproblem594.gif where A is a constant and http://img35.imageshack.us/img35/555/wangsnessproblem593.gif .[/URL] Find the...

Homework Statement Ok, here's the problem. It deals with the superposition of electric fields from uniformly charged shapes: A uniformly charged infinite plane is located at z = 0, with a surface density of charge σ. A uniformly charged spherical shell with the same surface density is located...

Homework Statement I was just wondering if I had done this problem correctly Take the rod axis to be the x-axis and the lefthand end of the rod to be x = 0. Assume lambda is not constant but that lambda = μx where μ is a constant. What are the units of μ? Find the force Vector F on the...

Homework Statement This is a three part problem. My first task is to calculate the divergence of \vec{r}/r^{a}. Next, I am to calculate its curl. Then I'm supposed to find the charge density that would produce the field \vec{E}=\frac{q\vec{r}}{4\pi\epsilon_{0}r^{a}} The Attempt at a...

Homework Statement A straight wire 7.0m long carries 30uC distributed uniformly over its length. What is the line charge density on the wire? _____ uC/m Homework Equations A) E = 2k/lamda / B) E = kq/r some other ones? The Attempt at a Solution I sub B into a...

Homework Statement Consider a cylinder, radius R and length L. Suppose the cylinder is charged with a volume charge given by P+P0 + Bz, where p0 and B are constants. Find the force on a charge Q at the center of the cylinder. Homework Equations E=q/4*pi*e*r^2 The Attempt at a...

Homework Statement We learned in E&M about the Dirac Delta function and its applications to representing the densities of point charges in space. For example, the charge density of space with a point charge q at the origin is given by q*delta(r). How does this density representation work with...