# Tagged Questions

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### Charge by Induction [on hold]

For example, Initially, there are two metal sphere touching each other and the ball on the left has a charge of +5q, while the other is neutral. Then a rod with charge -3q is brought near the left ...
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### Calculating the electrostatic energy per unit length of a cylindrical shell surrounded by a coaxial cable

Suppose an infinitely long cylindrical shell of radius $a$ carries a surface charge density $\sigma_0$ and is surrounded by a coaxial cable of inner radius $b$ and outer radius $c$ with uniform charge ...
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### Calculation of the electric field from a cube of charge with charge density proportional to radial distance [on hold]

I have a cube of side length $L$ centered at the origin and total charge $Q$; the charge density is $\rho(r)\propto r^n$ for some integer $n$, where $r$ is the radial distance in spherical ...
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### Force between two charges containing several dielectrics between them

The following question is quite similar to mine. Dielectric modification of electrostatic equations? However, the answer does not prove satisfactory to me. The formula given in the above problem ...
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### Product of ρ and φ [closed]

Consider a charge distribution $ρ_1(r)$ and the potential $φ_1(r)$ due to it. Consider another charge distribution $ρ_2(r)$ and $φ_2(r)$ due to it. Both distributions have finite extent, but are ...
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### Force exerted by a capacitor on a polar object

I was reading about capacitors and wondered what the force an electrostatic field created by a capacitor would be on an object with a certain charge and mass. If it can exert a force on a polar object ...
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### Electric field in two sphere system

Hi guys I'm really confused by this electric field question. Basically for the given setup shown, draw a graph of how electric field varies with distance from the center, given that radius of ...
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### Electrostatics kinematics equations (Coulombs Law)

If there are two similarly charged particles $Q$ and $q$ of masses $M$ and $m$, a Coulomb force is applied on each one (action-reaction). Suppose that $Q$ is stationary and we are shooting $q$ with an ...
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### How to prove Gauss's law div(E) = rho/epsilon from Coulomb's law? [duplicate]

As we know from coulomb's law that: $$\vec{E} = \frac{q}{4\pi\epsilon R^2} \hat{R}$$ using the above equation, how can I verify that: $$\vec{\nabla}\cdot \vec{E}=\frac{q}{\epsilon}$$ I have tried to ...
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### Finding electric field between overlapping surfaces [closed]

The problem is: A sphere with radius R is centered at the origin, an infinite cylinder with radius R has its axis along the z axis, and an infinite slab with thickness 2R lies between the planes ...
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### Are these assumptions correct?

Is it true:From equation $C=Q/V$ 1)If Potential difference is kept constant $C \propto Q$ 2)If charge is kept constant $C \propto 1/V$ Then if 2nd is true I do have a question: Don't we say that ...
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### Electric potential on a uniformly charged tube

A hollow cylinder, with no top or bottom, of radius $R$ and length $L$ is uniformly charged with density $\sigma>0$. I have to find the point on space where a point charge $q>0$ has to be drawn ...
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### Question related to Equipotential Surface

How will you show that equipotential surface is always directed perpendicular to electric field?
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### How to find the equillibrium points using Jacobian and Hessian?

Given that I have Jacobian and Hessian matrices of three particles interacting with each other in a harmonic trap through Coulomb's law in a 2D plane, how do I find the equilibrium points of them (I ...
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### Approximating electric field of two point charges

This is the question: ...
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### Apply Gauss' Law to find Electric Field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the ...
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### Issue with running a Van De Graaff generator

I am following this online video: http://www.youtube.com/watch?v=fsT69XnjxgU but my Van De Graaff generator is not working. I am using pvc pipes for the body, nylon and electrical tape as two rollers, ...
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### Gauss law from Gauss divergence theorem [duplicate]

Apply Gauss divergence theorem to the gravitational field due to a spherical object of mass M and uniform density located at origin. Obtain Gauss law for gravitation in integral and differential ...
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### Maxwells' equations and Coulomb's law

Coulomb's law and Maxwell's equations should be consistant as one can be derived from the other. Say we have a point charge with such a charge that $-kq=1$, meaning that at any point the electric ...
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### Force and Energy of interaction of conducting sphere and point charge

A completely isolated neutral conducting sphere of radius $R$ is kept such that its center is at a distance of $r\left(>R\right)$ from a point charge $+Q$. How can I find the force of ...
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### Surface charge density relation with the radius of curvature at the surface of a conductor [closed]

In a text book it was given that the surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. I didn't ...
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### Spherical harmonics

Given the following potential: $$V(\theta,\phi)=\frac{Q}{a}\left(\sin\theta \cos\phi+\frac{1}{2}\cos^2\theta\right)$$ on the surface of a sphere of radius $a$ I am trying to solve Laplace's Equation ...
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### Capacitors in parallel and dieletric [closed]

I'm trying to solve this problem: Two capacitors of capacitance $C_1=200pF$ and $C_2=1000pF$ are connected in parallel and loaded to a potential difference of $400V$. Subsequently the space ...
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### Show that the electric field, $\mathbf{\vec{E}}$ cannot be generated by any static distribution of charges

Show that the electric field $$\mathbf{\vec{E}}=\begin{pmatrix}0 \\ E_0x \\ 0\end{pmatrix}$$ where $E_0$ is a constant, cannot be generated by any static distribution of charges. I understand ...
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### Is this configuration correct for this spherical capacitor? [duplicate]

This capacitance contain 4 dielectric as shown in the figure dielectric 1 in half sphere and 2,3 in for 1/4 of the sphere and the fourth one in the last 1/4 of the sphere as shown and I want to find ...
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### Is there another way besides $V = k\int dq/r$ to find potential?

Suppose that the charge distribution $q(r)$ in the radial $r$-direction in a thin hollow disc of inner radius $a$ and outer radius $b$ is given by the power-law equation: q(r) = Q_0 \left[1 ...
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### The total energy of an electrostatic system

My problem is from Griffiths Introduction to Electrodynamics, Fourth Edition, p.112 Problem 2.60 (not homework): A point charge $q$ is at the center of an uncharged spherical conducting shell, ...
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### Motion of a dipole in an electric field

Assume that we have some non-constant electric field $E(x,t)$ and a point-dipole at a position $q$ with a constant dipole moment $\vec{p}$. How would you describe the time evolution, i.e. the motion ...
How do you derive the solution to Poisson's equation with a point charge source? Without using Coulomb's law or the electric field! To be more explicit, we have a point charge at $(0,0)$ of charge $q$ ...
There's an additional exercise from Introduction to Electrodynamics by Griffith. Problem 4.34 A point dipole p is imbedded at the center of a sphere of linear dielectric material (with radius $R$ ...