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Electric dipoles

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data
    The potential due to an electric dipole is V(r)=pcos(theta)/(4*PI*epsilon*r^2)
    Determine the direction of the electric field E at theta = 0 , 45, 90, 135 and 180 degrees?

    2. Relevant equations
    The field of an electric dipole is given by Er = 2pcos(theta)/(4*PI*epsilon*r^3)
    and E(theta) = psin(theta)/(4*PI*epsilon*r^3)

    3. The attempt at a solution
    I am a bit confused when look at the solutions to this question. For theta = 45 degrees is says that

    " Er = 2*E(theta) = sqrt(2)*p/(4*PI*epsilon*r^3) or alternatively
    Ez=p/(8*PI*epsilon*r^3) and E(x/y) = 3p/(8*PI*epsilon*r^3)
    so E = sqrt(5/2)*p/(4*PI*epsilon*r^3)
    at an angle to the dipole axis of alpha=72 degrees where tan(alpha)=3 "

    I am unsure why Er = 2*E(theta) and how that arrived at the direction of the dipole (especially how they determined it to be at an angle of 72 degrees!?!? )

  2. jcsd
  3. Apr 25, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Compare the formulas for Er and Eθ for θ = 45 degrees. Realize that sin(45) = cos(45).
    The are asking for the direction of the field with respect to the dipole direction, not the direction of the dipole.

    Given that Er = 2Eθ, first figure out (using a little trig) the angle the field makes with the radial direction (where θ = 45). The figure out its angle with respect to the dipole axis (which is where θ = 0).
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