Electrostatics Definition and 663 Threads

Homework Statement Find the distribution of charge giving rise to an electric field whose potential is $$\Phi (x,y) = 2~tan^{-1}(\frac{1+x}{y}) + 2~tan^{-1}(\frac{1-x}{y})$$where x and y are Cartesian coordinates. Such a distribution is called a two-dimensional one since it does not depend on...

Homework Statement There is a charged particle at height h over a circular area of radii R, then I have to calculate the capacitance. This is useful when somebody want to calculate energy harvesting, antennas, sensors that measures ions in plasma devices and particle accelerators...

Homework Statement (whole question/answer on IMG file also a scanned version in case) Hello, this question is from my notes and I couldn't figure out the graphing part of it. We're supposed to use limits and see what happens to the equations as x goes to infinity and zero. My question (as you...

Equation: ΣF=Σk(qi)(qj)/(r^2) Question: Considering more than a couple of particles. How can a net force on a charged particle be calculated if Coulomb's law is under the restriction of static forces? Thanks!

Homework Statement Homework EquationsThe Attempt at a Solution Potential at the center of conducting charged sphere surrounded by a grounded shell If I take another sphere of charge –q of radius a with uniform charge density, then the potential on the spherical region from the radius a to...

Homework Statement A point charge q is located a distance d meters from an infinite plane. Determine the electric flux through the plane due to the point charge. [/B] Homework EquationsThe Attempt at a Solution I consider another infinite plane at a distance d in the opposite direction. Now I...

Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. Homework Equations Gauss's law and symmetry The Attempt at a Solution I take 8 cubes...

Homework Statement Homework EquationsThe Attempt at a Solution I will try to choose the correct option using the common sense instead of solving it. As d decreases, the flux should increase. For R>>d, only option (a) and (d) satisfy this condition. Now, for choosing between (a) and (d)...

Homework Statement Homework EquationsThe Attempt at a Solution The energy stored in the capacitor is ## \frac { CV^2 } { 2 }##. So, this much energy will dissipate as heat. Hence, the correct option is (a). Is this correct? It doesn't depend on the shape of the capacitor, right? I have...

Homework Statement A force of 2.4N is exerted on a -1.8µC charge in a downward direction. What is the magnitude and direction of the magnetic field at this point? (The assignment sheet is called "Electrostatics Questions", hence the "Electrostatics?" in the title) Homework Equations Electric...

Homework Statement Hi I was wondering if anyone could give me a hand with this problem I'm trying to solve. I am trying to integrate this equation twice. I'm not really sure what to do with the right hand side of the equation.Homework Equations The Attempt at a Solution [/B] The left side...

Statement Four point charges, Q, -Q, Q, -Q, are placed at the four ends of a horizontal square of side a as shown in the figure above. What are the neutral points? The attempt at a solution The square is not exactly aligned parallel in its plane, say XY. So, the center is not a neutral point...

Homework Statement Two concentric cylinders with radii a & b (b>a) with an infinitely long grounded strip along the z-direction are given potentials \phi_1 and \phi_2. Find \Phi(r,\phi) for a<r<b Boundary conditions: \Phi(r,2n\pi)=0 \Phi(a,\phi)=\phi_1 \Phi(b,\phi)=\phi_2 Homework...

Homework Statement A force of 2.4N [L] is exerted on a -1.8x10-6C charge 0.2m away. What are the possible charges and locations of the second charge? Homework Equations FE= kq1q2 / d2 The Attempt at a Solution Rearranging the equation above for q2 is q2 = FE x d2 / kq1 and substituting...

Sorry it may seem that my question is a homework question but it is not since I have the solution of the problem. It is about obtaining Green function and using it to calculate the potential in space, provided the boundary conditions are satisfied. the questions are like below (It is a problem...

Homework Statement So I have an equation V = Ae(kx)+Be(-kx) And boundary conditons V= V0 when x=0 and V= 0 when x=b 2. Homework Equations I have solved ones where v=0 at x=0 where it nicely simplifies as the exponentials =1 and the Coeffecients A=-B which leads to a sinh function and I...

Dear all, I am trying to find the capacitance of a parallel plate structure that comprises a spatially varying (linear) dielectric in one dimension. I have two methods of solving this which give different answers, and I am not sure which is correct. I consider the dielectric region to be...

So, this has been bothering me for a few days and I'm having trouble understanding where the fault is. If we consider a uniform charge density ##\rho## extending through all space, then by symmetry, I would argue that ##\mathbf{E}=0## in all space. However, this does not agree with what a naive...

Ok, this might be a really dumb question, but I still am asking it: I was reading about gauss' Law when it comes to a hollow conductor with a (say) point charge inside it, and it seems intuitive to me that, in electrostatic equilibrium, the charges rearrange themselves to cancel the electric...

Homework Statement Two parallel plates of metal sandwich a dielectric pad of thickness d, forming an ideal capacitor of capacitance C. The dielectric pad is elastic, having a spring constant k. If an ideal battery of voltage V across its terminals is connected to the two plates of this...

Homework Statement The rectangular parallelepiped with sides ## a > b > c ## is filled with charge of constant density ## \rho ##. A sphere of radius ## 2a ## is constructed with its center at the origin. Find the flux through the surface of this sphere Homework Equations $$ \oint E \cdot...

Homework Statement An infinite non-conducting plate of thickness ##d## lies in the ##xy## plane. The bottom surface of the plate lies in the plane ##z=0##. The charge density of the plate is ##\rho=\rho_0 z /d~,~\rho_0>0##. Find the electric field in the regions ##z<0~~,~~0<z<d~~,~~z>d## and...

Homework Statement "Find the direction and the variables which the electrostatic field depends on at all points of the plane (xOy) uniformly charged with the density of positive charges ϱ" The Attempt at a Solution So first of all, I have to study the Invariances of symmetry. I tried to...

Homework Statement :[/B] Velocity of an electron at point A1 is Vo where cross sectional area is A. The velocity of electron at the end of contraction at point B where cross sectional area is 2A is V1.Find correct option a)V1< V0 b)V1= V0 c)V1> V0 d)V1<=V0/2 I have attached a picture of the...

Homework Statement two semi infinite grounded conducting planes make a 60 degree angle. One plane along the positive x-axis. There is a charge Q at point (m,n) located closer to the plate running along the x-axis than the other. what would a diagram look like with all image charges and angles...

1. Find the magnitude and direction of the force experienced by the charge of 3microcoulombs.Homework Equations After subtending forces of both the particles on the third one, we need to find the aggregate magnitude of the charge experienced by it. The Attempt at a Solution I was able to find...

Homework Statement : [/B]. in a milikan type experiment there are two oil droplets P and Q between the charged horizontal plates, as shown in the figure. Droplet P is in rest while Q is moving upwards. The polarity of charges on P and Q is: P. Q a). +. + b)neutral. -...

Homework Statement Derive following expression for the electrostatic potential energy of an electron in the field of a finite nucleus of charge, ##+Ze##, and radius, ##R=r_0A^{1/3}##, where ##r_0## is a constant. (Charge density is constant.) The potential we are asked to derive is: $$ V(r) =...

Question: If you charge a capacitor circuit and then separate the capacitor, does voltage increase beyond the initial source? It seams counter intuitive that if you plug a 9 Volt battery into two metal plates and pull the plates apart that you'll get massive voltage spikes, but that's what the...

Hi All, My question goes as follows: Suppose that, we charge a conducting very thin spherical shell in 'empty space' with a charge equivalent to 16 electrons. The radius (R) of the shell is 20 light years. We wait 20+ years for the electrons to reach equilibrium. Then, we approach one electron...

Homework Statement hi i was doing a practice physics junior olympiad paper when i got stuck in question 11 in this link [/B] https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf Edit by moderator: Inserted relevant extract of the PDF so that helpers do not have to...

Homework Statement Find the Electric field a distance z above one end of a straight line segment of length L that carries a uniform line charge λ Homework Equations Complicated formula due to lack of font for the notation used by the author of the book. so I wrote it out. I did my best to...

Homework Statement For the system given, both objects have the same charge and same mass (both given). I'm also given string length, L. I need to solve for θ. Homework Equations Coulomb's Law, W=mg The Attempt at a Solution Using simple equilibrium force analysis (with weight, tension, and...

Homework Statement As always, I wish I were allowed to upload a drawing ;) This is not a problem, this is a derivation of sorts, so I don't have any numbers. I have 3 points. one at the origin, a point charge q and a test charge Q I have a vector from the origin to the point charge q with a...

Homework Statement this is a theoretical question.please consider the situation as follows: we are charging a metallic sphere using induction phenomenon with the help of a postively charged metallic rod and while on grounding the electrons flow from the ground to the sphere rather than sphere...

Homework Statement In the figure particles 1 and 2 are fixed in place on an x axis, at a separation of L = 7.30 cm. Their charges are q1 = +e and q2 = -27e. Particle 3 with charge q3 = +3e is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force on...

We know that the attractive force between the opposing poles of identical permanent magnets is a product of their field strength and that the total force diminishes as the distance between them increases. If we assumed the magnets to be point entities, the formulation is the same as that for...

Hey everyone Just a picture of my configuration. The assumption here is $$\epsilon_a,\epsilon_b,\epsilon_c$$ are different from one another. Really the interest of this problem is to find the scalar potential $$\phi$$, such that $$\nabla^2 \phi = 0$$. So now my question, about jump...

Homework Statement An infinite line of charge with charge density λ is parallel to and a distance d above an infinite grounded conducting plate. What is the charge density σ that is induced in the plate? For simplicity, consider the line of charge to lie along the line x = 0. Homework...

Homework Statement A grounded Z-axis symmetric closed conductor has a single point charge at the origin within it, inducing negative charge onto its inner surface. Given the induced charge density from the unit point charge, find the surface charge induced instead by a unit dipole at the...

Homework Statement We are given a disk with negligible thickness, a radius of 1m, and a surface charge density of σ(x,y) = 1 + cos(π√x2+y2). The disk is centered at the origin of the xy plane. We are also given the location of a point charge in Cartesian coordinates, for example [0.5,0.5,2]. We...

Hello everyone! 1. Homework Statement Calculate the work needed to move a point-charge with the charge q from infinity to the center of the chargedistribution given by: \rho(\vec{r})=\rho_0 e^{-\alpha r} Homework Equations U=qV V=\frac{1}{4\pi\epsilon_0}\int_{V}\frac{\rho(\vec{r})}{r}dV The...

I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons...

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...

Homework Statement A sphere of radius ##a## is non-uniformly charged on its surface with a charge whose surface density is ##ρ_s(φ)=ρ_{so}(cosφ)^2## where ##φ## is the angle measures from the z axis, (0≤φ≤π) and ##ρ_{s0}## is a constant. Determine the expression for the total charge distributed...

Homework Statement [/B] My problem is in figuring out how to solve number 22 through 23, particularly getting the set-up done. Homework Equations Newton's law of gravitation and coulomb's law of accelerationThe Attempt at a Solution [/B] I initially misread the question and thought that...

Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...

Homework Statement A pith ball is charged by contact with a Van De Graaff machine, and is repelled away from the dome. It remains at its location. Using the chart given, what is the mass of the pith ball? Distance between centre of generator and pith ball...

Homework Statement Find the expression for the electric field at point M(a,a,0) if the linear charge density is known ( ##Q'## ) Homework Equations 3. The Attempt at a Solution [/B] I tried something like this and would like your feedback on it. I separated the triangle into three parts...

Homework Statement In the picture below it is asked that i calculate the resultant electric field if the linear charge density is known. Calculate the resultant electric field of a charged semicircle wire (positioned as in the picture) at some point M on the Z axis if the linear charge density...