# Questions tagged [method-of-images]

A method to solve certain differential equations on a domain by putting image sources outside the domain to fulfill [boundary-conditions] on the boundary. Common applications can be found in [electrostatics], [magnetostatics] or [acoustics].

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### Gauss's Law vs Image charges

Consider a grounded shell of radius $R$, inside is a point charge $q$ at a distance $a$ from the centre. Now, this charge would induce an amount of charge $-q$ on the conductor, whose field would be ...
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### Why does method of image work with multiple plates too?

I was solving this : A point charge is placed between two semi infinite conducting plates inclined at an angle of 30 degrees. The number of images is? The correct answer is 11, which you get by ...
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### Method of images and Laplace Equation

In the method of images Section in the Griffiths' Electrodynamics A classic image problem is used to illustrate the significance of the of the uniqueness theorem.the whole point is about if a solution ...
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### Method of images and the zero potential of the conductor

I was reading the method of images in Griffiths' electrodynamics book. He uses the classic image problem to explain the significance of the uniqueness theorem suppose a point charge $q$ is held a ...
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### Mirror image Electric field and potential

pg My book says the electric field due to a positive point charge at a certain distance from the surface of flat, infinite earthed conductor can be obtained by introducing a virtual negative mirror ...
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### Fundamental physical concept behind inductance of a long wire above a ground plane

Please explain the underlying physics concept behind the inductance of a long wire above an infinite ideal ground plane. Sometimes the image method is used and sometimes the coupled magnetic flux ...
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### Potential inside metal sphere in field of external charge [closed]

If a have a arrangement like-( Where r is radius of hollow conducting sphere with centre C and Q is point charge) Then what is potential at any point between P and C? I think first we need to find ...
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### Why Can The Charge Distribution of A 2D Conductor Be Determined By Flattening Its 3D Counterpart?

The most famous instance of this trick is probably in the case of finding the surface charge distribution of a charged conducting disc, where this disc can be perceived as a squashed down version of a ...
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### Do conductor plates encloising charged particles exert a force on one another due to the charges induced on them? How to calculate in a 1D model

I would very much appreciate some guidance on the below. Consider a one-dimensional world as depicted in the attached figure. We have two (lets say positively charged) particles enclosed by two ...
1 vote
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### 'Thin' conducting plate ambiguity

The situation at hand: We have an infinite, thin conducting, grounded ($V=0$) plate at $z=0$. Point charge (with charge +$Q$), at $z = a$. How exactly are the charges distributed? I used the method ...
1 vote
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### Conflicting lensmaker's equation representation

I keep finding these two conflicting forms of the lensmaker's equation. I understand that (n2-n1)/n1 is the same as (n-1) if referring to a lens in air, but I can not make sense of why the reciprical ...
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### Method of image charges for electric potential in a metallic disk

It is well known that the method of image charges is not always applicable, so I was wondering: is there an analytic way to calculate the electric potential for a point charge interacting with a ...
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### Charge conservation and the physical significance of image charges

I am confused by the physical significance of image charges. A similar question has been asked about the fact that image charges add up to the total charge in the conductor, which I think is ...
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### Can the formula for a conductor be applied to a grounded infinite conductor plate?

I'm studying about Image method with "Introduction to electrodynamics-Grffiths" And, this book explains the process finding the induced surface charge density when a point charge $q$ is held ...
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### Using method of images on ungrounded spheres

I have recently learnt how to calculate the induced charges on a grounded sphere using the method of images. However, in all of the examples I did, the conductor itself is grounded, so I am wondering ...
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### Method of images for currents?

This is a question that uses an “image current configuration” What exactly is the motivation for using the method of images on a current setup. The proof I’ve seen for uniqueness theorums was the one ...
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### Two-body problem + shield

Let us consider two point charges, one positive, one negative, interacting via Coulomb force. In the absence of any other force, this system constitutes an elementary example of two-body problem, and ...
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### Distant pairs of charges becoming neutral

This is a standard question in EM where you have 2 pairs of charge. When you connect opposite charges with the wires, then we get essentially 2 conductors with net 0 charge. Now thanks to the ...
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### Is there a simple, intuitive reason for why the total induced charge is always equal to the hypothetical image charge in the method of images?

In the method of images, the total induced charge (actual) on the surface of the conductor is always equal to the image charge (hypothetical). Can this be explained intuitively?
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### Why doesn't electric field pass through an infinite grounded conducting sheet?

Consider the diagram. Why doesn't the electric field cross the infinite conducting sheet. I understand if it was a closed conductor, the electric field inside would be 0 due to the electric field ...
1 vote
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### Symmetry in the method of images for a charge and a conducting sphere

This is a doubt on the method of images from J.D Jackson's Classical Electrodynamics first edition, Chapter 2. While trying to find the potential of the configuration of a conducting sphere and charge,...
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### Induced surface charge and total charge in method of images [closed]

In David j Griffith's introduction to electrodynamics section 3.2 example 3.2 author calculate the potential above a grounded sphere such that a charge q is placed above the sphere at a distance a ...
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### Two ray ground reflection model to predict antenna performance over conducting ground

I have an antenna that is placed at a certain height over conducting ground plane. If it's measured, I could imagine ripples in a farfield pattern owing to reflection from the ground. Is it correct to ...
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### Why must we use the method of image to calculate the surface charge density? [closed]

A point charge $Q$ is brought to a position a distance $d$ away from an infinite plane conductor held at zero potential, now calculate the surface-charge density induced on the plane. The book always ...
1 vote
156 views

### Is this conducting plate charged?

Setup 1: the grounded case When a positive point charge is near a conducting grounded infinite plate of finite thickness, the area near the charge becomes negative. The net charge on the plate should ...
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### Why is a charge induced on a grounded metallic plate when another charge is placed near it? Why doesn't the charge flow into the ground?

When we bring a charge -Q close to a plate some positive charge is induced on the near surface of the plate to this external charge and some negative charge on the other farther surface. I believe ...
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### Is there a mirror charge method to solve a half-space conductor with finite potential?

I came across a problem in electrostatics that I couldn't find a solution for, so I was hoping someone could answer my problem. The setting is a usual mirror charge problem, with a point charge $q$ at ...
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### Energy due image charges

Consider a point charge located above an infinite, grounded, conducting plane. The potential everywhere above the plane is the same as that of the image charge (located below it). Why is it wrong to ...
1 vote
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### When to use Method of Images for electrostatic field problems?

I have been solving some questions regarding electrostatic fields, and I'm not quite sure when and when not to apply the method of images. As I understand it, 'method of images' is simply replacing ...
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### Electric potential boundary condition in method of images

In Griffiths, and Purcell and Morin, it is mentioned that the convention that the zero of potential is at infinity may fail when a charge distribution extends to infinity. In the problem of a point ...
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### Energy between multiple source and image charges near perfect conductors

Imagine two charges $q_1$ and $q_2$ near a infinite conductive plane. They will induce spherical distribution of charge on the plane, which - as it is commonly known - simulated by introduction of two ...
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### Do other methods exist than the method of image charges for computing equipotential field at surface around charged objects?

I am trying to find another method for robotics based on "attractive-repulsive" forces s.t. first object forms the target to reach and the second one (and others) forms the obstacle to avoid....
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### Method of images [closed]

we know this classic problem shown. Where a conducting infinite sheet has a charge q in front of it at distance d. We know how to solve this using method of images for the region A where the charge q ...
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### Why is method of image charges not working?

suppose a situation with two infinite thin conducting planes in front of each other with one of them having a charge density σ it can be clearly predicted that the induced charge density on neutral ...
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### Why do I have to divide the total work in the method of images? [closed]

I got that potential, field and force don't need division since as long as it satisfies the boundary conditions it is correct as the answer is unique due to the uniqueness theorem. But what qualities ...
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### Understanding the method Mr feynman said in the lecture regarding method of images

In the feynman lectures ,this was given related to method of images : We have solved, for example, the field of two point charges. Figure 6–8 shows some of the field lines and equipotential surfaces ...
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### Showing the existence of two spherical surfaces to indirectly prove the method of images working in the setup of a charge and a spherical conductor

I was trying to show that in the field lines of the setup of two charges lets say $q_1$ and $q_2$ ,distance between then is $z$ where $q_1q_2 <0$ . We can always draw two imaginary spherical ...
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### A point charge between two grounded parallel conducting planes

Consider a point charge between two grounded parallel conducting planes $V=0$. Let the first plane be at $x=0$, the second one at $x=D$ and the charge be at $x=x_0$. Like in a double mirror, the total ...
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### Point charge above a ground plane without images

Suppose one wanted to find the electric field around a point charge located above an infinite ground plane as in the classic method of images example, but without using the method of images itself. (I....
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### Factor of 2 difference in force using image charges?

Consider a point charge $q$ a distance $z$ from an infinite grounded conducting surface in the $xy$-plane. Using the method of images, we know that the potential $V$ can be found in the region $z>0$...
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### Calculating work in an Image dipole method

I have encountered an Electromagnetism problem, which asked me to calculate the total work required to separate an electric dipole from a conducting plane. The dipole's moment was given $p$ and the ...
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### Understanding Green's function in the mirror charge method

Initially I want to point out that there are many way as to how we can define the green's function in vacuum or when other objects are taken into consideration, and the same goes for the Potential in ...
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### Are image charges uniquely determined by a problem setup?

can two image charge configurations satisfy the boundary conditions of a problem and thus produce the same electric field in the region of interest?
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### Why am I not allowed to put the image charge in the region where I want to calculate electrostatic potential?

I just want a rigorous explanation to why I'm not allowed to put an image charge in the region where I want to calculate the electrostatic potential. I know intuitively why it's true, but in Griffith'...
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### Electrostatic potential created by two finite-width infinite-length strips at opposite potential $\pm V_0$

I'm tackling with this problem but it seems I'm going in the wrong direction. Consider a 3D space where the potential is specified over the plane $z=0$ , assuming it has value $V_0$ and $-V_0$ on ...
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### Electric Potential for a Point Charge and an Infinite Conducting Plane on the Other Half-Space

In the book titled "Modern Electrodynamics" by Zangwill, on chapter 8, there is a discussion on the electric potential of a system of an infinite conducting plane and a point charge ...
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### Image charge inside dielectric with complex permittivity?

A common textbook problem in electromagnetism is to place a point charge $q$ outside a dielectric material with permittivity $\epsilon$ . In the case of a semi-infinite dielectric material, the ...
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Suppose I have two charged solid conducting spheres, both given a charge $Q$ and are separated by a distance a. The force between them should be $\frac{Q^2}{4\pi\epsilon_0 a^2}$. Is it correct? ...