Total charge Definition and 62 Threads

Assume that a certain charge distribution ##\rho## generates an electrical field ##E_{ext}## in the surrounding space. We also note the corresponding generated potential ##V_{ext}##. Assume furthermore that a conductor A, with a definite shape and volume, is placed in field ##E_{ext}##, and is...

I first tried to use the Gauss' law equation E.A = q/ε0 to find the total charge enclosed. The answer came out to be q(enclosed) = 4πqε0e^(-4r). So for r approaching infinity, q(enclosed) approached 0. Next, I tried the equation ∇·E = ρ/ε0, calculated rho to be -4qε0e^(-4r)/r^2 and total...

Homework Statement Homework Equations gauss law The Attempt at a SolutionI got D. Integral ( E dot da) = q(enc)/ e0 E is constant so iit can come out and the angle between them is zero (cos(0)=1 |E| integral (da) which gives me |E| a where a=4 pi r^2 c *(r/e0) * 4 pi r^2 q(enc)= c*4*pi*r^3

Hello, I am unsure whether this is in the right place, I do think this is nuclear physics however, I was hoping I could get some idea of whether I am answering this question correctly as unfortunately I won't be able to attend the class that explaining this concept. 34eV of energy, are lost...

Homework Statement A static charge distribution has a radial electric field of magnitude ##E = \alpha \frac{e^{-\lambda r}}{r} ## where λ and α are positive constants. Calculate the total charge of the distribution. Homework Equations Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...

Homework Statement Consider an infinite environment with electrical permittivity non-homogeneous $$\epsilon=\epsilon_0(1+a/r)$$ a being a positive constant. A conducting sphere of radius R and charge Q is put on that environment, centered at r=0. Determine the electric field $$E$$, the...

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...

The question asks to find total charge in a region given x has lower bound 0 - upper bound 5 , y has lower bound as 2 and upper bound as 5. Based on knowledge I have been reading throughout the chapter, I set up a double integration with those dxdy, but the results went out to be off - compared...

Hi I am confused about an example in my textbook related to charge stored by a capacitor A 100 uF capacitor and a 700 uF capacitor are placed in series, along with a cell of 3V. Calculate the p.d. across the 100 uF capacitor. The book states the solution as follows: "Using the reciprocal...

Homework Statement An infinite plane in z=0 is held in potential 0, except a square sheet -2a<x,y<2a which is held in potential V. Above it in z=d there is a grounded plane. Find: a) the potential in 0<z<d? b) the total induced charge on the z=0 plane. Homework Equations Green's function for a...

Homework Statement A point charge ##q = 30 mC## is located in the center of a conductor spherical shell with an internal radius of ##a = 10 cm## and an external radius of ##b = 20 cm## and total charge null. Find the surface density charge of both the internal surface and external surface of...

Hi I hope this the right place to put my question I didn't understand how it became like this Thank you

Homework Statement Find the total charge Q given the charge density ρ(r)=ε0A(4πδ3(r)-π2e-λr/r The Attempt at a Solution I know the solution's steps start with: Q=∫ρdr=ε0A(4π∫δ3(r)dr-λ2∫e-λr(4πr2)/rdr) What I don't understand is where that 4πr at the end comes from. That last step is only...

Homework Statement We have a discharge tube where the cathode is a cylinder with radius a and the anode is a coaxial cylinder with radius b, a<b. Both cylinders have length L, (Note that L can not be seen as large).The potential of the cathode is 0 and the potential of the anode is U>0. The...

Homework Statement Hey guys, So the title pretty much says it. I have to find the total charge density produced by all the electrons in a closed subshell where n = 3 and l = 2. The charge density produced by a single electron is (-e)|R_{32}(r)Y_{2,m}(\theta , \phi)|^{2}Homework Equations So he...

In this image, C1 is 1 microfarad and C2 is 3 microfarads and both capacitors are charged with a potential difference of V = 100V. S1 and S1 are closed. The solution says this is in parallel, but I don't see how it is. It looks like it's set up in series to me. But even if it is in...

Problem: In a neutral He atom consisting of a positively charged nucleus of charge ##2q## and two electrons each of charge ##-q##, the volume charge density for the nucleus and for the single electron cloud are respectively given by \rho_n(\vec{r})=2q\delta^3(\vec{r}) and...

Homework Statement In some region of space, the electric field is \vec{E} =k r^2 \hat{r} , in spherical coordinates, where k is a constant. (a) Use Gauss' law (differential form) to find the charge density \rho (\vec{r}) . (b) Use Gauss' law (integral form) to find the total charge...

Homework Statement A hollow metal sphere has inner and outer radii of 20.0 cm and 30.0 cm, respectively. As shown in the figure, a solid metal sphere of radius 10.0 cm is located at the center of the hollow sphere. The electric field at a point P, a distance of 15.0 cm from the center, is...

Homework Statement A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 24-g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 26^{\circ} angle with the vertical, what total charge Q must have been applied to...

I've just worked out using the method of images that the total induced charge on a grounded hollow conducting sphere in the presence of a dipole outside the sphere pointing in the radial direction is non-zero. I can't think of an intuitive explanation as to why a dipole outside would induce a...

For a certain problem I have non-zero electrical field E, non-zero electric flux density D, and non-zero volumic charge density ρV. When I integrate pV dV over the given region, I get 0. How is this possible?

how do you prove that the electric field is determined uniquely from knowing the total charge on a conductor (just the outline of the proof). Thanks!

Homework Statement A solid sphere of radius a rotates with angular velocity ω\hat{z} relative to an inertial frame K in which the sphere's center is at rest. In a frame K' located at the surface of the sphere, there is no electric field, and the magnetic field is a dipole field with M=M\hat{z}...

Homework Statement The cylindrical drum of a copy machine is .38 m long with .05 m radius. If charge is uniformly distributed over the cylindrical surface (the top and bottom flat circular ends of the drum have no charge) and the electric field very close to this surface midway along the...

Homework Statement Using integration calculate the total charge on the sphere radius R Volume charge density at the surface of the sphere p0 p = p0r/R I started with dq = 4*pi*r^2*dr*(p0r/R) but i am not sure how to integrate (in terms of what variable I would assume r=0 to...

Hi everyone-This is my first time posting a homework question. I'm a little stuck. I appreciate any help to clue me in the right direction. Homework Statement If the drum has a surface area of 6.25×10−2 , what total quantity of charge must reside on the surface of the drum? I got...

Homework Statement A point charge q is embedded at the centre of a sphere of linear dielectric material (with susceptibility chi(subscript e) and radius R). b)What is the total charge on the surface? [3 marks] c) where is the compensating negative bound charge located? calculate it...

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...

In the attached picture is all of the information to complete this problem. The picture is of a solid sphere at the center of a hallow sphere, both of which are conductors. The question asks to find the total charge of the exterior and interior surfaces of the hollow conductor, as well as the...

Homework Statement I was given a sphere with radius R and a charge density function δ(r),where r is the distance from the center of the sphere. I want to find the total charge in the sphere. Homework Equations I know that Q = δV The Attempt at a Solution I tried integrating V...

Homework Statement Consider two point charges a distance 1.5 cm apart. These charges have an electric potential energy of -190 micro J. The total charge of the system (the sum of the two charges) is 26 nC. What is the charge of each point charge? Homework Equations Uelec = K*q1*q2/d...

Homework Statement Surface charge density on gold plate of radium 15cm is 5x10^-9 C/m^2 A) Calculate electric field intensity (E) near plate center B) Assuming surface charge density is constant over the entire surface of the plate, calculate the total charge on the plate Homework...

And if so, How? From the post 15 and 16 of the thread https://www.physicsforums.com/showthread.php?t=474719" But total charge and total current, Q and I, do form a 4-vector, don't they? There seem to be two ways to solve this, but I can't figure out which one is right. Properly...

Initially a 1.52 µF capacitor and a 2.63 µF capacitor are connected in parallel, with 9.80 V across their plates. The two capacitors are not connected to anything else. The connecting wires are then reversed on the terminals of one capacitor, so that the positive plate of each capacitor is...

Homework Statement Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density. (a) Calculate the total charge contained in a segment of...

Homework Statement I am given a charge density for a solid sphere \rho=14.1\frac{pC}{m^{3}}\frac{r}{R} The r is the distance from the center of the sphere and R is the radius of the whole thing. R=5,6cm Now I am asked for the whole charge contained by the sphere.Homework Equations...

I'm trying to find the total charge on a conducting surface but am stuck at the last part of this integral. Maybe I'm just dumb but it looks really complex to me and I can't seem to figure it out. http://www.flickr.com/photos/54479402@N07/5045800952/#/photos/54479402@N07/5045800952/lightbox/...

Homework Statement We have a sphere (radius R) where charge is placed inside of it, ρ(r)=ρ0 cos(θ/3) sin(φ/2). Find the total charge. Your answer will be in terms of R and p0. Homework Equations The Attempt at a Solution I think I did it correctly, but I would just like to...

Homework Statement We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box? Homework Equations The Attempt at a Solution I have an...

Homework Statement A total charge of 7.47x10^-6 C is distributed on two different small metal spheres. When the spheres are 6.35 cm apart, they each feel a repulsive force of 15.5011 N. How much charge is on each sphere? Homework Equations F=k Qq/r^2 Q1+Q2=7.47x10^-6C The Attempt...

Homework Statement Given V(r)=\frac{Q}{4\pi \epsilon_0}\frac{1}{r+a}, find the total charge. Homework Equations \overline{E}=-\nabla V \rho=\epsilon_0 \nabla \cdot \overline{E} \rho=-\epsilon_0 \nabla^2 V The Attempt at a Solution I started out by finding the charge density \rho from...

Homework Statement The current at the terminals of the element in an ideal basic circuit element is i = 0, t < 0; i = 20e(-5000t) A, t \leq 0 Calculate the total charge ( in microcoulombs) entering the element at its upper terminal. Homework Equations The...

Homework Statement What is the total charge of all the electrons in 1.77 Kg of H20? Homework Equations I really just lost on how to do this problem as I missed school today. Any help would be greatly appreciated The Attempt at a Solution the 1st step I took was trying to find...

total charge lifted by the "charge escalator" Homework Statement A 1.5 V flashlight battery is connected to a wire with a resistance of 5.00 ohms. The figure shows the battery's potential difference as a function of time. The slope is linear going from (0, 1.5 V) to (2 hrs, 0)...

Homework Statement A 1.5-volt, AAA cell supplies 750 milliamperes of current through a flashlight bulb for 5.0 minutes, while a 1.5-volt, C cell supplies 750 milliamperes of current through the same flashlight bulb for 20. minutes. Compared to the total charge transferred by the AAA cell...

I am having two metal sheets which are curved and fitted on the outer sides of a pipe. A 9V pottential is applied to both the plates. Dimensions of the plate = 130mm X 65mm (L X B) How can i find the charge distribution on the plates to find the total charge. I need this to calculate the...

Homework Statement Given the Electric flux density of \vec{D}=\frac{100xy}{z^{2}+1}\vec{u_{x}}+\frac{50x^{2}}{z^{2}+1}\vec{u_{y}}+\frac{100x^{2}yz}{(z^{2}+1)^{2}}\vec{u_{x}} C/m^{2} find the total charge inside a tiny sphere with a radius of r=1\mu m centered in c(5,8,1).Homework Equations...

[b]1. A closed surface with dimensions a = b = 0.400 m and c = 0.600 m is located as shown in the figure (be aware that the distance “a” in the figure indicates that the rectangular box sits a distance “at” from the y-z plane). The electric field throughout the region is nonuniform and given...

Homework Statement A thin insulating rod of length L is placed such that its end point is distance R away from a semi-infinite insulating line. The line has linear charge density \lambda. The rod has charge Q. Both are distributed uniformly. What is the force exerted on the rod? Define Q_o...