MAW: 27 JAN. 2017 LEARNING MAXWELL DIFFERENTIAL +Integral forms. CONTD.

27 JAN. 2017 LEARNING MAXWELL DIFFERENTIAL +Integral forms. CONTD.

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James Clerk Maxwell (1831 - 1879) - Find A Grave Memorial

James Clerk Maxwell

Gauss's laws

Gauss's Law. The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field.

Gauss's Law - Hyperphysics

hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

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Gauss's Law - Hyperphysics

hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

Gauss's Law. The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field.

‎Gaussian Surfaces · ‎Electric Field, Line Charge · ‎Electric Field · ‎Area Integral

Gauss's law - Wikipedia

https://en.wikipedia.org/wiki/Gauss's_law

where Φ_E is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within V, and ε₀ is the electric constant. ... Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.

Faraday's law of induction - Wikipedia

https://en.wikipedia.org/wiki/Faraday's_law_of_induction

Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction.Eq. 3 is obtained from Faraday's law.

‎History · ‎Faraday's law · ‎Proof of Faraday's law · ‎"Counterexamples" to Faraday's law

Faraday Law of Electromagnetic Induction | Electrical4u

www.electrical4u.com/faraday-law-of-electromagnetic-induction/

In 1831, Michael Faraday, an English physicist gave one of the most basic laws of electromagnetism called Faraday's law of electromagnetic induction. This law ...

Magnet moves towards the coil‎: ‎Deflection in g...

Position of magnet‎: ‎Deflection in galvanometer

Magnet moves away from the coil‎: ‎Deflection in ...

Magnet at rest‎: ‎No deflection in galvanometer

Faraday's law - Richard Fitzpatrick

farside.ph.utexas.edu/teaching/em/lectures/node43.html

Faraday's law. The history of humankind's development of physics can be thought of as the history of the synthesis of ideas. Physicists keep finding that ...

Ampere's law
Eq. 1 & 2 are obtained from Gauss laws of electric & magnetic fields.

Eq. 3 is obtained from Faraday's law.
Eq. 4 is obtained from Ampere's law.

hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html

Ampere's Law. ... Ampere's Law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.

‎Magnetic Force Between Wires · ‎Solenoid Magnetic Field · ‎Magnetic Field

Formulation in SI units convention

Name	Integral equations	Differential equations	Meaning
Gauss's law	$\oiint$ ${\scriptstyle \partial \Omega }$ $\mathbf {E} \cdot \mathrm {d} \mathbf {S} ={\frac {1}{\varepsilon _{0}}}\iiint _{\Omega }\rho \,\mathrm {d} V$	$\nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}$	The electric flux leaving a volume is proportional to the charge inside.
Gauss's law for magnetism	$\oiint$ ${\scriptstyle \partial \Omega }$ $\mathbf {B} \cdot \mathrm {d} \mathbf {S} =0$	$\nabla \cdot \mathbf {B} =0$	There are no magnetic monopoles; the total magnetic flux through a closed surface is zero.
Maxwell–Faraday equation (Faraday's law of induction)	$\oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} }{\mathrm {d} t}}\iint _{\Sigma }\mathbf {B} \cdot \mathrm {d} \mathbf {S}$	$\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$	The voltage induced in a closed circuit is proportional to the rate of change of the magnetic flux it encloses.
Ampère's circuital law (with Maxwell's addition)	$\oint _{\partial \Sigma }\mathbf {B} \cdot \mathrm {d} {\boldsymbol {\ell }}=\mu _{0}\iint _{\Sigma }\mathbf {J} \cdot \mathrm {d} \mathbf {S} +\mu _{0}\varepsilon _{0}{\frac {\mathrm {d} }{\mathrm {d} t}}\iint _{\Sigma }\mathbf {E} \cdot \mathrm {d} \mathbf {S}$	$\nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right)$	The magnetic field induced around a closed loop is proportional to the electric current plus displacement current (rate of change of electric field) it encloses.

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Who is James Clark Maxwell ?

James Clerk Maxwell (1831 - 1879) - Find A Grave Memorial

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Hla Myint Gauss law illustration.
Maxwell collected ideas of Gauss, Ampere , Faraday & presented them in a composite picture of electromagnetic field.

MAW

Friday, January 27, 2017

27 JAN. 2017 LEARNING MAXWELL DIFFERENTIAL +Integral forms. CONTD.

Gauss's Law - Hyperphysics

Gauss's Law - Hyperphysics

Gauss's law - Wikipedia

Faraday's law of induction - Wikipedia

Faraday's law - Richard Fitzpatrick

Formulation in SI units convention

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