A question about cruel and electric fields?

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sagar474

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is curl of a study electric field is zero in every case ?

then how the expression
delXE=-dB/dt

that is an electric field can produce a time varying magnetic field ?

how the time varying magnetic field is related to delxE with out involving time variable on left side of the equation.
 


\[{ \nabla }{\times} E= - \frac{\partial (B) }{\partial (t)} \]

Curl of time varying electric field is not zero

.
 
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If there is no change of Magnetic field B ,then curl of E is Zero .
 
with out considering the magnetic field, can we calculate the curl of electric field ?
 

Yes you can calculate the Curl of Any Vector Field ,
 
then the curl of study electric field at any point should be zero.
then why curl of time varying electric field is not zero?

curl depends up on time? no !
 

Stationary charge --E field only
Charge in motion -E field and B Field


Consider a Stationary positive charge ,stationary positive charge produces E Field only ,and calculate the Curl of the Electric field
you find it to be zero .
 
Yes ,it's already proved
 
{Induced emf }

\[V_{emf}= N \frac{\mathrm{d} \psi}{\mathrm{d} t}\]


\[V_{emf}=- \frac{\mathrm{d} }{\mathrm{d } t} \int_s{ B . ds}\]

\[V_{emf} = \oint_{L} E {\cdot} dl\]

\[V_{emf} =\oint_{L} E { \cdot}dl=-\int_S \frac{\partial(B)}{\partial (t) }.ds\]

therefore Applying Stokes theorem and simplifying
\[ \nabla {\times} E=-\frac{ \partial (B) }{ \partial (t)}\]

---------- Post added at 12:10 ---------- Previous post was at 12:03 ----------

Some other Interesting links

From Feynman proof of Maxwell equations to noncommutative quantum mechanics
h**p://iopscience.iop.org/1742-6596/70/1/012004/pdf/jpconf7_70_012004.pdf

Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
h**p://arxiv.org/abs/hep-th/0308079
 

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