Pdf image theory for electrostatic and magnetostatic. What is an intuitive explanation of the method of images in. Then the standard surface charge calculation applies the boundary condition. Method of images in electrostatics wolfram demonstrations.
Mcdonald joseph henry laboratories, princeton university, princeton, nj 08544 november 21, 2009. Wednesday homework 2 electrostatics tuesday homework is to be uploaded to ecampus by 11. Introduction image problems in electrostatics refer to boundaryvalue problems that specify some charge distribution in a volume bounded by a closed surface and also specify the potential on the same surface. A charge q is on the xaxis a distance x from the midpoint of the dipole. Apr 09, 2016 the vector form of coulombs law of electrostatics gives us the direction of force along with its magnitude acting upon two charges.
The method of image charges also known as the method of images and method of mirror charges is a basic problem solving tool in electrostatics. The mathematical techniques that we will develop have much broader utility in physics. Notice, however, that for most electrostatic boundary problems the images do. More details can be found in griffiths book introduction to. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem see dirichlet boundary conditions or neumann boundary conditions. Feb 17, 2015 the intuitive explanation of the method of images is that the images are not real charges but fictitious charges chosen to mathematically replace physically real charges in order to simplify the mathematical derivation. Coulombs law of electrostatics the vector form youtube. The image charges must be external to the volume of interest. The method of images is most often employed in electrostatic. Method of images and expansion in orthogonal functions 2.
Electrostatic problems with solutions and explanations. For these two examples, the image method fully deserves its name. Find materials for this course in the pages linked along the left. Two identical objects, separated by a distance d, with charges equal in magnitude but of opposite signs exert a force of attraction of 2. Lecture 2 solving electrostatic problems todays topics 1.
Applying gausss theorem show that for a spherical shell, the electric field inside a shell vanishes, whereas outside it, the electric field is as if all the charge has been concentrated at the centre. Uniqueness theorems in electrostatics laplace and poisson. If electrostatics problems always involved localized discrete or continuous distribution of charge with no boundary conditions, the general solution for the potential 3 0 1 4 dr u sh c c. The classical example of the application of this method is the problem of a point charge at a distance d from a grounded perfectly conducting in. Department of mathematics, simon fraser university, bumaby, british columbia, canada v5a is6 and h. Let us examine the completely different configuration, consisting of the point charge q together with another point charge r.
The method of image charges is a basic problemsolving tool in electrostatics. In this section we will use method of images to solve several prob lems. It must be worked must be on the printout of the pdf of the assignment available in ecampus. Apply this theorem to calculate the electric field due to an infinite plane sheet of charge. There are three possible boundary conditions that assure this result. Physics electrostatics problems science and mathematics education research group supported by ubc teaching and learning enhancement fund 20122015. The electrostatic field of a point charge and an electrical dipole in. Method of images the method is based on the fact that any solution of poissons equation that satisfies the appropriate boundary conditions is the unique solution. Analogy of grounded conducting sphere image problem with. Here we present an alternative image charges method that is.
Illustrated below is a fairly general problem in electrostatics. The electrostatic field to calculate the force exerted by some electric charges, q1, q2, q3. Grahamstown 6140, south africa rccciwd february 1984. In spherical coordinates, the laplace equation reads. It is convenient to formulate the problem by means of spherical coordinates, with the origin of coordinates at the center of the sphere. What force do these objects exert on each other if the distance between them becomes 2d. Potential the potential due to the charges q and q v. Image theory for electrostatic and magnetostatic problems involving a material sphere article pdf available in american journal of physics 611. The assignment must be right side up and easily readable.
But the problems which you should use image methods or any further like greens formula etc. Study of electricity in which electric charges are static i. In the classic image problem of electrostatics an infinite conducting planar sheet and a point charge above the sheet, one calculates the potential and hence field in the region above the conducting sheet. The differential transform and its application to an. In this two dimensional problem we take the axis of the cylinder to be z axis, and the. In this twodimensional problem we take the axis of the cylinder to be z axis, and the.
Analogy of grounded conducting sphere image problem with mirroroptics 2 1. We need to find the images of the charge in the spherical surface which encloses it. Wednesday homework 2 electrostatics tuesday homewo. Very powerful technique for solving electrostatics problems involving charges and conductors. If we touch two spheres to each other, find the final charges of the spheres. If the voltage is known on a closed surface dirichlet. The boundary condition, can be satisfied by an image charge q inside the sphere zb. Murrell department of computer science, rhodes university. The simplest possible set of images would be a single. In this case, the image is another point charge with reversed algebraic sign at a distance d below. The vector form of coulombs law of electrostatics gives us the direction of force along with its magnitude acting upon two charges.
Under certain favorable conditions, it is possible to apply the method of images, in which one or more image charges of specified magnitude can be strategically placed to enable the laplace equation with the given boundary conditions to be more easily solved. Classic electrostatics image problem surface charge physics. Basic electrostatics classical mechanics newtonian, lagrangian, hamiltonian mechanics quantum mechanics wave mechanics wave function and born probability interpretation schrodinger equation simple systems for which there is an analytical solution free particle particle in a box, particle on a ring. Using the superposition principle, the force on q3 is 23 323 22 23 0 23 1 4 qq qq rr fff r r ggg in this case the second term will have a negative coefficient, since is negative. Idea is to convert a seemingly difficult electrostatic problem involving spatially extended charged objects e. I mean there should not be any boundary conditions and for such systems gauss law can be used in any problem. If one has found the initially undetermined exterior charge in the second problem, called image charge, then the potential is found simply from coulombs law, x z. Dielectric and magnetic image methods 1 problem 2 image. What is the electric force on q due to the dipole and how does this force behave in the limit x d dipole approximation. Boundaryvalue problems in electrostatics i reading. Then the solution to the second problem is also the solution to the. There would be no need of the poisson or laplace equations.