
[NOTES/EM02014] Flux  Example of a point chargeNode id: 5961pageThe flux of the electric field of a point charge placed at the centre of a sphere is explicitly computed and shown to be
\[\text{Flux} = \frac{q}{\epsilon_0 }\] 

231018 20:10:01 
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[NOTES/EM02012] Dipole in Uniform Electric FieldNode id: 5957pageWhen a dipole is placed in a uniform electric field, it experiences a torque given by \(\vec \tau= \vec p \times \vec E\). 

231018 19:10:38 
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[NOTES/EM02010] Gauss Law and Use of SymmetryNode id: 5956pageGauss law aloe is not sufficient to determine the electric field for a given system.To determine electric field using Gauss law the symmetry of problem plays an important role by determining the direction of the electric field in given problem. 

231018 19:10:36 
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[NOTES/EM03008]Maxwell's Second Equations from Coulomb's LawNode id: 5645pageMaxwell's equation, \(\nabla \times \vec{E}=0\), can be easily proved by direct computation of curl of electric field of a point charge and appealing to the superposition principle. 

231018 15:10:52 
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[NOTES/EM03007]Work done in field of a point chargeNode id: 5644pageWe discuss the path independence of the work done by static electric field. This leads to, as in mechanics, introduction of the electric potential. An expression of the electric potential is derived by an explicit computation of work done by on a unit positive charge by the electric field of a point charge \(q\). For an arbitrary distribution of charges, the electric potential is obtained by making use of the superposition principle. 

231018 14:10:17 
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[NOTES/EM03006]Electrostatic Energy of a Uniformly Charged Solid SphereNode id: 5643page The electrostatic energy of a uniformly charged solid sphere is computed by computing the energy required to bring infinitesimal quantities and filling up the sphere. 

231018 13:10:39 
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[NOTES/EM03005]Multipole Expansion of PotentialNode id: 5642pageThe large distance expansion of potential due to a localized charge distribution is obtained. The first three terms receiving contributions from the monopole, the dipole moment and the quadrupole moment are explicitly displayed. Important properties of dipole and quadrupole moment are discussed. 

231018 08:10:38 
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[NOTES/EM03003]Maxwell's Equations from Coulomb's Law Node id: 5637pageStarting with the Gauss law and using divergence theorem of vector calculus we derive Maxwell's first equation $\nabla\cdot \vec{E}= \rho/\epsilon_0$. 

231018 08:10:34 
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[NOTES/EM03002]Electrostatic EnergyNode id: 5635pageExpressions for electrostatic energy of system of point charges is derived. 

231018 08:10:36 
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[NOTES/EM03004]The Electric Stress TensorNode id: 5641pageAn expression for the electric stress tensor is derived for a charge distribution in a volume \(V\). The surface integral of the stress tensor gives the total electric force on the charge in the volume \(V\). 

231017 14:10:45 
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[NOTES/EM03001]Computation of Electric PotentialNode id: 5634pageThe curl free nature of the electric field in electrostatics implies existence of a potential,\(\phi(\vec(r))\), from which the electric field can be derived as \(\vec{E}=\nabla \phi\). The potential at a point is just the work done in moving a unit point charge from infinity to its current position. 

231017 14:10:31 
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[NOTES/EM02015] Proof of curl free nature of \(\vec E\)Node id: 5960page$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$ Starting from Coulomb's law a proof is given that the electric field of a system of point charges obeys the Maxwell's equation. \[\nabla \times \vec E =0\] 

231012 19:10:59 
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[NOTE/EM02014] Flux of Feld of a Point ChargeNode id: 5959article 

231012 19:10:58 
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[NOTES/EM02013] Solid AngleNode id: 5958pageIn this section the concept of solid angle is defined as a generalization of angle in plane geometry 

231012 17:10:14 
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[NOTES/EM02009] Line Integrals In PhysicsNode id: 5955pageA few examples of problems are given from electromagnetic theory and other areas of physics are given in which the line integral appears. 

231012 17:10:01 
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[NOTES/EM02007]Maxwell's Equations for ElectrostaticsINode id: 5579pageThe Gauss law of electrostatics follows from the Coulomb’s law for a point charge and superposition principle. The Gauss law along with the Gauss divergence theorem of vector calculus imply Maxwell’s first equation \(\nabla\cdot\bar{E}=\rho/\epsilon_0\) for electrostatics 

231010 20:10:14 
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[NOTES/EM02008]Maxwell's Equations for ElectrostaticsIINode id: 5580pageThe Gauss law of electrostatics follows from the Coulomb's law for a point charge and superposition principle. The Gauss law along with the Gauss divergence theorem of vector calculus imply Maxwell's first equation \[ \nabla\cdot\bar{E}=\frac{\rho}{\epsilon_0}. \] for electrostatics. 

231010 20:10:28 
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[NOTES/EM02006]Proof of Gauss LawNode id: 5578pageThe Gauss law of electrostatics follows from the Coulomb’s law for a point charge and superposition principle. The proof given here follows Feynman’s lectures. It makes use of two important features of the electric field due to a point charge. These are (i) the magnitude of the field obeying the inverse square law, and (ii) radial direction of the electric field of a point charge. The above two properties are essential to the proof. Gauss law will not hold for hypothetical field, not having both the properties. 

231009 04:10:51 
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[NOTES/EM02004]Applications of Gauss LawNode id: 5570pageGauss law is applied to compute the electric field for several systems, see the Table of Contents for details. The symmetry of the problem is used in a nontrivial manner to arrive at the answers for the electric field. 

231007 05:10:29 
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[NOTES/EM02003]Electric Field due to Continuous Charge DistributionsNode id: 5568pageElectric field due to several charge distributions, listed in the table of contents, is computed using Coulomb’s law. 

231007 05:10:47 
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