, wherem→" role="presentation">m⃗ is the magnetic moment of the loop. For a planar loop|m→|=" role="presentation">|m⃗ |= current×" role="presentation">× and the equation∇×B→=μ0j→" role="presentation">∇×B⃗ =μ0j⃗ and is given by
[NOTES/EM-07001]-Electric CurrentNode id: 5707In this section we compute the leading term in the magnetic field of a current loop at large distances and obtain an expression for the magnetic moment of the loop.
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[NOTES/EM-07002]-Current ConservationNode id: 5708
The equation of continuity for conservation of electric is derived. An expression for current in a wire is obtained in terms of number of electrons per unit volume.
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[NOTES/EM-07007]-Cross product ruleNode id: 5712in this section the rule about the direction of cross product the cross product of two vectors is explained.
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[NOTES/EM-07008]-Magnetic Vector PotentialNode id: 5713The vector potential is introduced using the Maxwell's equation ∇×B→=0" role="presentation">∇×B⃗ =0 |
is derived. The expression for the magnetic field is obtained as volume integral, the Biot Savart law, is derived. The expressions for the magnetic field for the surface current and the line current are given.
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[NOTES/EM-07009]-Magnetic Field of a Current Loop at Large DistancesNode id: 5714In this section we compute the leading term in the magnetic field of a current loop at large distances and obtain an expression for the magnetic moment of the loop.
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[NOTES/EM-07010]-Magnetic Field of a Current Distribution at a Large DistancesNode id: 5715For a volume distribution of current an expression for magnetization density,{\it i.e.} the magnetic moment per unit volume, is obtained. An expression for the magnetic field at large distances, in terms of magnetization density, is derived.
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[NOTES/EM-07011]-Direction convention for Ampere’s LawNode id: 5716Direction convention for Ampere's law is explained
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[NOTES/EM-07012]-Biot Savart LawNode id: 5717The Biot Savart law for current carrying wire is explained.
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[NOTES/EM-07013] Equation of Continuity and RelativityNode id: 5919
The equation of continuity appears in different branches of physics. It represents a local conservation law. In order to be consistent with requirement if special relativity every conserved quantity must come with a current which gives the flow of the conserved quantity across a surface and the two must obey equation of continuity. In this section we discuss these aspects of conservation laws.
" role="presentation"> |
[NOTES/EM-07014] Conservation Laws for Electromagnetic FieldsNode id: 5998" role="presentation"> |
[NOTES/EM-07015] Current Density --- ExamplesNode id: 5988 |
[NOTES/EM-07016] Force on a Line and Volume Element of a WireNode id: 5989Expressions for force on line and volume elements of a current in magnetic field are derived. |
[NOTES/EM-07017]Node id: 5997The magnetic moment for a point particle is shown to be related to the angular momentum ℓ" role="presentation">ℓ |
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[NOTES/EM-07018] Poisson Equation for Vector Potential.Node id: 5991 |
[NOTES/EM-07019] Solving for Vector PotentialNode id: 5992" role="presentation"> |
[NOTES/EM-07020] Charge ConservationNode id: 5993The meaning of charge conservation is discussed. It is known to be mathematically represented by the equation of continuity. It is argued that special relativity requires that there should be a 'current' associated with every conserved quantity. |
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4727:Diamond Point