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I Calculating Induced Electric field

  1. May 2, 2017 #1
    In class we were trying to calculate the induced electric field created by changing the magnetic field stregth.
    Imagine theres a circular surface which magnetic field out of the screen.Since we are changing the magnetic field from Faraday's Law there should be a induced current or charge flow simply.To create this motion we need electric field.So he drew another circle inside the outer surface with radius r Here is the pic
    Adsız.png
    Then he said lets suppose theres a charge on the point P.And he explained the Electric Field and direction etc.And He said lets suppose It rotates once the circle

    Now then He did something like this;

    ##W=qε=\int {\vec{F}⋅d\vec{r}}##
    ##W=qε=Eq2πr##
    ##ε=E2πr## Then he used Faraday's Law and we found the E field.
    I am stucked cause
    ##W=qε=\int {\vec{F}⋅d\vec{r}}## should be zero.Cause it comes to same point.
    ##W=\int_p^p {\vec{F}⋅d\vec{r}}=0##
    He never used ##\oint##
    What am I missing ?
    If were used closed integral like ##\oint_p^p q\vec {E}⋅d\vec{r}=Eq2πr## ?

    I think He should use closed integral.
     
    Last edited: May 2, 2017
  2. jcsd
  3. May 2, 2017 #2

    Charles Link

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    Homework Helper

    The induced electric field from a changing magnetic field is not a conservative field. Electrostatic fields (conservative fields) satisfy ## \nabla \times E=0 ## so that ## \oint E \cdot ds=0 ## by Stokes law. This is not the case for the induced ## E ## field because ## \nabla \times E=-\frac{dB}{dt} ## so that by Stokes law ## \oint E \cdot ds=-\frac{d \Phi_m}{dt} ##. And yes, your instructor should use ## \oint ## for this integral.
     
  4. May 2, 2017 #3
    I understand , thanks a lot :)
     
  5. May 5, 2017 #4

    vanhees71

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    2016 Award

    Well, of course in Stokes's theorem the line integral is around a closed path. Otherwise it's wrong. Why one should need an extra symbol, I however don't know ;-).
     
  6. May 5, 2017 #5
    Its more nice,I like it :p
     
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