Elecrostatics Definition and 104 Threads

The volumetric charge density is given as $$\rho(r) = \rho_0 \left(1 - \frac{ar}{R}\right)$$ What shall be the Electric field at any distance ##r## ? My approach was to directly use the coulomb's law and integrate with respect to volume. $$ \mathbf{E}(\mathbf{r}) = \frac{1}{4\pi\epsilon_0}...

Consider a scenario in the picture where one half of space consists of a material with permittivity ϵ1 and the other half consists of a material with permittivity ϵ2, where ϵ1 > ϵ2. A unit positive charge is fixed at the interface between the two materials. Path1 is entirely within the material...

We are given a conducting solid sphere, and it is cut by a plane which has a minimum height r/2 from the centre of the sphere, which has radius r. A charge Q is given to the smaller part of the conductor, and it is required to find the induced charge on the curved and flat surfaces of the other...

We have a system of two unequal oppositely charged point charges, of which ##q_2## is smaller and ##d## is the distance between charges. There is an equipotential spherical surface of potential ##V=0## that encloses a charge of lesser absolute value. The task is to find parameters of that...

So consider you have a point charge ##q_1## which is somehow fixed in space so it won't move if a force is applied to it. Then at some distance away you have another point charge ##q_2##, where ##q_1## and ##q_2## are of comparable magnitude (so, one is not insignificant compared to the other)...

My friend said 'you missed the negative sign the second time you wrote integral of Edr in the right hand side in your second line'. But if put a negative sign it would mean that potential decreases when travelling against ( antiparallel) to field, which is wrong

Why don't electrons leave the metal surface? I have searched the internet for the answer and from my teachers they all say that electrons are attracted to the positive ion crystal lattice. I know that, but the problem is why is that attraction so much greater than the repulsion from other free...

I am using an old monitor (MITSUBISHI RDT27IWLM). The power consumption changes when the screen is white or black, but does the frequency of the weak electromagnetic waves emitted from the monitor change? Or is the frequency the same, only the output is stronger/weaker?

Part (a) was simple, after applying $$Q=\int_{\mathbb{R}^3}^{}\rho \, d^3\mathbf{r}$$ I found that the total charge of the configuration was zero. Part (b) is where the difficulties arise for me. I applied $$V(\mathbf{r})=\frac{1}{4\pi \epsilon _0}\int_{\Gamma }^{}\frac{\rho...

I am finding the potential everywhere in space due to a point charge a distance 'a' on the z-axis above an infinite xy-plane held at zero potential. This problem is fairly straight forward; place an image charge q' = -q at position -a on the z-axis. I have the solution in cartesian coordinates...

I can calculate the electric field strength at any point above the plane with Gauss' Law (##E = \frac{\eta}{\varepsilon_0}##) and so the electric potential at any point a perpendicular distance ##z## above the conducting plane (##V=−\frac{\eta}{\varepsilon_0}z##). But I'm having trouble taking...

It's not a homework. I came up with this problem myself. Trying to understand fundamentals of electronics. Do you know how to solve it? Is voltage somehow related to electron energy levels? What knowledge should I gain to be able to solve problems like that? Thank you! If we ground the cathode...

I've been able to prove the following inequality $$\frac{2\pi\epsilon_0}{\log\left(\frac{b_1b_2}{a_1^2}\right)}\leq C \leq \frac{2\pi\epsilon_0}{\log\left(\frac{a_1a_2}{b_1^2}\right)}$$ but have no clue how to obtain exact value. Can someone check whether this inequality is correct and show how...

Phi = int of (3xi^ + 4j^).vector dA = 3 int of(xdA) Now we put x= 3 and we get at last 36 N m^2/C. I am getting confused why E is a fuction of x. How can that be? How can we represent the E and position x on the same coordinate system. Is it right ? Because we know distance is inversely...

For a uniform field like this, I imagine the two plates that creates it are made of multiple atoms with charges, which are points sources that create radial fields. We know that radial fields don't have parallel fields lines, so how are parallel fields lines form when the field is made of...

According to a popular book on electrodynamics a special case of electrostatics is- ''source charges are stationary (though the test charge may be moving)''. My question is- now that the test charge is moving, how is it a special case of electrostatics anymore? Also many times we deal with...

When I plug in the numbers I get ##2.9513\cdot 10^{-5}C/m^2##, not ##17.6\cdot 10^{-6} C/m^2##. Can someone point out where I'm going wrong?

I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..

The force per unit area (Pressure) on a part of the sphere is given by F = (E outside + E inside)/2 * Q = 0.5 (kQ/R^2) * (Q/ 4piR^2) = (Q^2/ 32pi^2 e0 R^4). I understand the above line. The solution then says this pressure is exerted on the contact area between the 2 spheres, as given by...

Hi, I found the following question in a physics book, and so dusted off my 30yr old knowledge on capacitors and tried to answer it. The question is as follows :- "Suppose two nearby conductors carry the same negative charge. Can there be a potential difference between them? If so, can the...

In my book, the potential gradient for a charge placed anywhere in space is defined as: E = -V/r HOWEVER, for parallel plate (capacitors) the potential gradient is defined as E = V/d (V being the potential difference). How come there's no negative sign for the potential gradient of the parallel...

1- Write down the complete MAXWELL equations in differential form and the material equations. 2- An infinitely extensive area is homogeneously filled with a material with a location-dependent permittivity. There are charges in the area. Give the Maxwell equations and material equations of...

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...

figure 1: → I don't understand how to approach this problem. Basically it asks for the distance r.I think I should use Gauss's law, but I've been thinking about the shape of the gaussian surface and I'm not sure about how it should look or where I should place it. Any help would be useful...

This is not a homework question but something that bugs me a bit. My professor has stated that the electric field inside a conductor is 0. This I understand. However, he has also said that even if the conductor has some hole in it, the electric field inside this hole is also 0 Now, two...

so I recently finished the basics of classical mechanics and decided to start with electrostatics/dynamics, I started with Griffiths but found pretty challenging should I just persist and continue with it or maybe go through the Feynman lectures(vol2) or electricity and magnetism by Purcell and...

In Jackson,(3rd edition) Chapter 1 , page no, 44 He uses the word "semipositive definite" what is it? is it "non-negative" definite?

I don't understand why moving charge doesn't affect the magnitude of induced charge. Could someone explain why it is possible? Thanks in advance.

I'm trying to understand how the total electric field changes as it passes through layers with different electrical permittivities and conductivities (as shown in the linked figure). The rectangular prism layers are assumed to be very thin. The conductivities ##\sigma## and relative...

I am trying to calculate the interaction energy of two interpenetrating spheres of uniform charge density. Here is my work: First I want to calculate the electric potential of one sphere as following; $$\Phi(\mathbf{r})=\frac{1}{4 \pi \epsilon_{0}} \int...

r_{13}=r_{23}=\sqrt{(30*10^{-3})^2+(90*10^{-3})^2}=\sqrt{9*10^{-3}}\\ F^E_{13}=F^E_{23}=9E9\cdot\frac{5*10^{-9}\cdot3*10^{-9}}{9*10^{-3}}=1.5*10^{-5}\\ \theta=tan^{-1}(\frac{90*10^{-3}}{30*10^{-3}})=71.565\,degrees\\ \vec{F}^E_{13}=<F^E_{13}cos\theta, F^E_{13}sin\theta> = <4.743*10^{-6}...

Hello, If you have an appropriately oriented conductive ring in a constantly changing magnetic field, current will flow in the ring. There will also be a magnetic field associated with the current in the ring. I understand (maybe ... ) that the current is due to the electric field which is...

Equivalent capacitance before and after remains the same. Now the 10F capacitor (which was initially connected in parallel with 20F) would have 30 C charge. Hence an additional 20C must have been supplied to it. The only path which may supply the charge is through battery. However this leads...

Merged thread deleted first post next post is the first post.

What would the fact that the fifth surface is connected to the ground imply: that V(r=R_5)=0 or that \sigma _5=0?

Assume that an infinite metallic plate A lies in the xy-plane, and another infinite metallic plate B is parallel to A and at height z = h. The potential of plate A is 0, and the potential of plate B is constant and equal to V. So, there is a uniform electrostatic field E between plates A and B...

Summary:: if Plate A had a potential of 9V, This means as We approach a unit charge from +Infinity to A we have to do this precise amount of work Now we remove plate A, And replace it with plate B that has a potential of -9V Again that means to go from +Infinity To B we actually gain energy, or...

If a charge was placed inside an electric field, where the electric field was equal to zero, what effect would the charge have?

I have an infinite sheet (in lossless, homogeneous medium) of time-harmonic current in ##yz##-plane at ##x=−d##. The current density on this sheet is given by $$\mathbf{J}=\hat{z}J_0\delta(x+d)$$ ##δ(x+d)## is delta function. Moreover, there is a perfect electric conductor (PEC) half space at...

I am having trouble solving the following problem. I am given two positive charges on the x axis: I know that the electric field strength at point P is ##E=150 \frac{V}{m}##, ##d=1.8m## and ##a=2.5m##. I want to find the charge of ##Q##. As far as I know, the electric field on the y-axis...

I came across an example of a solution to finding the potential of a charged layer using the Green function (here, pdf). The standard algorithm for finding the Green function by boundary conditions for many problems is understandable: \begin{align*} G_\mathrm{Left} = Ax+ B \\ G_\mathrm{Right} =...

I know that ##B = \mu n I## and ##\phi = B \pi R^2##. So with have ##d\phi / dt = \mu n \alpha \pi R^2##. But I don't know what to do with this? is this the answer? I don't think so but I don't know what to do after this.

I know how Gauss law helps us to calculate the discontinuity at a point on the surface of a surface charge. Similarly using Gauss law, is there a way to determine the continuity at other points of electric field due to a surface charge or the continuity at all points of electric field due to a...

I got the answer: E(P)=(k*Q)/(3î )−(k*Q*ĵ) /2 Can someone confirm if this is the right answer?

An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains finite. Now how can we have a continuous electric dipole volume distribution from such a...

Hi, I've a question about electricity in the following scenario: consider an accumulator (e.g. a 9V battery) and an analog/digital voltmeter having a probe connected to the accumulator + clamp and the other to the ground (for instance connecting it to a metal rod stuck in the ground). Do you...

Homework Statement Imagine having a conducting sphere with free charge ##Q## surrounded by a spherical shell filled with a dielectric and then a conducting spherical shell with no free net charge. I want to find out the charge induced on the spherical conducting shell by the sphere or by the...

Homework Statement Consider the following system: which consists of a conducting sphere with free charge , a dielectric shell with permittivity ##\epsilon_1##, another dielectric shell with permittivity ##\epsilon_2## and finally a conducting spherical shell with no free charge. Homework...