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Determine whether vector field is magnetic or electrostatic

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Three vector fields are listed below. Determine whether each of them is electrostatic field or magnetic field.


    2. Relevant equations
    F1(x, y, z) = A (9yz ex + xz ey + xy ez)
    F2(r,∅,z) = A [(cosx/r)er + (sinx/r) e]
    F3(r,θ,∅) = Ar2 e(-r/a) er


    3. The attempt at a solution
    Used matrix to determine the first one
    | ex ey ez |
    |δ/δx δ/δy δ/δz|
    |yz xz xy |
    as electrostatic (curl = 0 = -δB/δt) & fine with the how & what defines an electrostatic field
    but . . . .
    not sure how to determine whether one of these fields is magnetic or not!

    Help please.
    Thank you.
     
  2. jcsd
  3. Apr 10, 2013 #2

    ehild

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    Homework Helper
    Gold Member

    What do you know about the divergence of the electric and magnetic fields?

    ehild
     
  4. Apr 10, 2013 #3
    1. divergence should be proportional to the density of magnetic "charge" (div B = 0 - no monople law)

    2. div E = ρ / E0
    (and for a conservative (electrostatic) field the curl should be zero. (Faradays law - curl E - -∂B/∂t))

    The difference is that I "get" 2 and can show this by the matrix I showed above, but not sure how to apply 1 to come to the conclusion of whether it's an electrostatic field or magnetic field.

    Can I go down a similar route to find that divB = 0
     
    Last edited: Apr 10, 2013
  5. Apr 10, 2013 #4
    OK, OK I've kicked off a bit early.
    I will be using the equations booklet & make sure I look at it to complete problems in the way I've been taught (although coming back to it from a while ago dulls the mind if you're not using it).
     

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