
[YMP/EM03009] Electrostatic Energy of a Parallel Plate CondenserNode id: 6028page 

231204 23:12:46 
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[YMP/EM03006] Potential of a solid sphereNode id: 6027page 

231204 23:12:16 
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[YMP/EM02010] Electric Field of Overlapping Uniformly Charged SpheresNode id: 6023page
Problem
Two spheres, each of radius $R$ and carrying charge densities $+\rho$ and $\rho$ respectively, are placed so that they partially overlap. The separation between the centers of the spheres is $D$. Show that the field in the region of overlap is constant and find its value. 



231204 05:12:08 
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[LECS/EM03002]Examples of Computation of Electric PotentialNode id: 5652pageWe give details of computation of potential for the following examples. 1. Uniformly Charged Ring 2. Uniformly Charged Disc 3. Thin Spherical Shell 4. Uniformly Charged Solid Sphere 

231128 16:11:52 
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[LECS/EM03003]Electrostatic EnergyNode id: 5653pageThe electrostatic energy of a continuous charge distribution is defined as the energy required to assemble the charges at infinity into the positions as in the given distribution. For a continuous charge distribution it is shown to be \( \dfrac{\epsilon_0}{2}\iiint(\vec E\cdot\vec E) dV\) . Thus a volume of space having nonvanishing electric field has energy density \(\dfrac{\epsilon_0}{2}(\vec E\cdot\vec E)\).The expression for the electrostatic energy reduces to the usual answer \(\frac{1}{2} CV^2\) for a charged parallel plate capacitor. For a uniformly charged sphere of radius \(R\) the electrostatic energy is proved to be equal to \(\frac{3}{5}\Big(\frac{Q^2}{4\pi\epsilon_0 R^2} \Big)\). 

231128 16:11:21 
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[LECS/EM03001]Electric PotentialNode id: 5651pageThe concept of electric potential for static electric field is defined as work done on a unit charge. The expression for the electric potential of a \(q\) charge is obtained. For a system of point charges the potential can be written down as superposition of potential due to individual charges. As an illustration we compute potential due to a dipole. 

231128 15:11:04 
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[LECS/EM03004]Multipole ExpansionNode id: 5654pageLarge distance expansion of electric potential of a charge distribution in a finite voluem \(V\) is presented. Expressions for dipole and quadrupole moments are obtained. 

231128 15:11:03 
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[LECS/EM03005]Maxwell’s Equations for ElectrostaticsNode id: 5655pageThe Maxwell's equations for electrostatic are derived from Coulomb's law which has been formulated based on experiments. This provides initial experimental evidence for the Maxwell's equations. We discuss two applications of Maxwell's equations. The first result is that the electric field inside an empty cavity in conductors is proved to be zero. The second result is an expression for electric stress tensor is derived. The surface integral of the electric tensor gives the force on charge distribution.


231128 15:11:01 
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[LECS/EM02003] Gauss LawNode id: 6025pageThe flux of electric field through a surface in defined as a surface integral and the statement of Gauss law is given. A few examples of computing the electric field using Gauss law and symmetry of the problem are discussed. A simple and intuitive proof of Gauss law is given following Feynman lectures. The task of proving Gauss law for arbitrary charge distribution is reduced to the problem proving the Gauss law for a single point charge by appealing to the superposition principle. 

231127 12:11:56 
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[LECS/EM02001] Coulomb's Law and Electric FieldNode id: 6012articleThe Coulomb's law gives the force between two point charges. It can be reformulated as giving electric field of a point charge which in turn gives rise to force on a nearby point charge.The electric field of a point charge is generalized to system with continuous charge distributions. Expression for the electric field of line surface and volume charge distiibutions are given. The examples of computation of electric field of (a) Line charge, (b) Uniformly charged loop, (c) Thin Spherical Shell and (d) Dipole are discussed.


231127 11:11:16 
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[YMP/EMAll] Solved Problems in Electromagnetic TheoryNode id: 5918collectionWork Under Progress
(LUPDate : Nov 24, 2023)


231126 18:11:08 
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[FeynIISec14]Node id: 6026page 

231124 10:11:27 
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[YMP/EM02012] Average Value of Electric FieldNode id: 6021pageProblem
A solid sphere of radius \(R\) carries a charge density \(\rho(\vec{r})\). Show that the average of the electric field inside the sphere is \[\vec{E}=  \frac{1}{4\pi\epsilon_0} \frac{\vec{p}}{R^3},\] where \(\vec{p}\) is the total dipole moment of the sphere. 

231123 22:11:27 
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[YMP/EM02011] Overlapping Spheres IINode id: 6024article
Problem Two spheres each of radius $R$ are placed so that they partially overlap. The charge densities in the overlap region is zero and in the two non overlapping regions is $+\rho$ and $\rho$ respectively as shown in figure. The separation between the centers of the spheres is $D$.Find the electric field in the two nonoverlap regions. 



231123 22:11:38 
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[YMP/EM02009] Electric Field of a Uniformly Charged SphereNode id: 6022page
Show that the electric field of a uniformly charged sphere, radius \(R\), total charge \(Q\) has the magnitude given by\[E= \begin{cases} E_0 x & x< 1 \\ E_0/x^2 & x>1 \end{cases}\]where \(E_0= \dfrac{Q}{4\pi\epsilon_0 R^2 }\) and \(x=\dfrac{r}{R}\).


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231123 22:11:47 
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[YMP/EM02008] Electric Field Due to a DipoleNode id: 6013pageA dipole is a system of two equal and opposite charges separated by a distance. Its electric field is computed and the field at large distances depends only on the dipole moment, defined as the product of the charge and separation between the charges.
While dipole is a system of two charges, the concept of dipole moment is defined and is useful for any system of charges with total zero charge. 

231123 22:11:57 
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[YMP/EM02007] Electric Field of a Uniformly Charged Spherical ShellNode id: 6020page 

231123 22:11:50 
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[YMP/EM02006] Electric Field due to a Uniformly Charged DiskNode id: 6019pageWe compute the electric field due to a uniformly charged disk at a point on the axis of the disk. 

231123 22:11:28 
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[YMP/EM02004] Electric Field due to a Line with Uniform Charge DensityNode id: 6016pageLet \(AB\) be a line charge with charge per unit length $\lambda$, which is given to be uniform. The field is to be computed at a point \(P\),. Let \(p\) be the perpendicular distance of \(P\) from the line \(AB\). let \(\alpha, \beta\) be the angles as shown in the figure. Electric field will be calculated at a general point \(P\), the corner point \(C\) and the middle point \(M\) as shown in figure below.


231123 22:11:35 
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[YMP/EM02003] Dipole Moment of Overlapping SpheresNode id: 6015page
Two spheres each of radius $R$ are placed so that they partially overlap. The charge densities in the overlap region is zero. Outside the overlap region but inside the spheres the charge densities in the two non overlapping regions are $+\rho$ and $\rho$, respectively, as shown in figure. The charge density in the overlap region will be zero. The separation between the centers of the spheres is $D$. 

 Guess the value of the dipole moment?
 Compute the dipole moment of the system and check the correctness of the expression you guessed.
 How will the dipole moment change if the two spheres equal and opposite total charges but have different radii \(a,b, a \ne b\).


231123 22:11:53 
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