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Directions of (electro)magnetic fields/application of right hand rule

  1. Nov 12, 2013 #1
    Hello everyone,

    I have two different problems from webassign homework that I could use some clarification with; as stated in the title, I'm having trouble applying the right hand rule in both. Since the basis of my difficulties are the same, I hope it's okay to include both problems in the same thread. Here's how I've learned the right hand rule, I'm hoping it's correct:

    Thumb = Direction of electric charge/current/velocity vector/propagation of wave
    Fingers, pointed outward forming a 90° angle with thumb = Direction of magnetic field vector
    Palm, facing outward = Direction of Lorentz force vector/electric field

    1. The problem statement, all variables and given/known data

    1.) A 2.10 m length of wire is held in an east-west direction and moves horizontally to the north with a speed of 15.3 m/s. The vertical component of Earth's magnetic field in this region is 40.0 µT directed downward. Calculate the induced emf between the ends of the wire and determine which end is positive.

    2.) Consider an electromagnetic wave traveling in the positive y-direction. The magnetic field associated with the wave at some location at some instant points in the negative x-direction as shown in the figure below. What is the direction of the electric field at this position and at this instant?

    Figure: https://www.webassign.net/sercp9/21-mcq-001.gif

    2. Relevant equations

    None

    3. The attempt at a solution

    #1. The answer to the bolded part of the question is the west end is positive. The wire is moving upwards, so my thumb goes upwards. Since the magnetic force of the Earth is going downward, I would think I would point my fingers downward, but since this is not anatomically possible does downward entail pointing my fingers in the negative direction on the z-axis/fingers into the screen? Thus, my palm would be facing west, and the west end is positive. Is my understanding right here?

    #2. The answer is the negative z-direction. Thumb goes to the right on the y-axis in direction of the propagation vector (c), B-field/fingers goes into the screen in the negative x direction, and so my palm is facing up in the positive z-direction...However, this is not the answer. What am I doing wrong?

    Thanks!
     
  2. jcsd
  3. Nov 12, 2013 #2

    rude man

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    In this case I prefer to think of the physics of the situation:

    Think of a positive free charge in the wire. There is a force F = qv x B applied to that charge. So that charge will bunch up in the + end of the wire.

    So, setting up a coordinate system with x east, y north, and disregarding magnitudes,
    v = j
    B = -k
    F = j x -k = -i

    I don't think the right-hand rule is particularly illuminating in determining emf direction. It depends on memorizing a formula. Anyway, your answer is correct.

    Again, I would resort to algebra:
    you know that the poynting vectror is
    P = E x H.

    So let the unknown E field unit vector be labeled ζ.

    Then, j = ζ x -i
    which is satisfied if
    ζ = -k.

    So yes, your answer is wrong. It's pointing downward.

    I ralize this doesn't help you understand the right-hand rule, but there is nothing sacred about it. And it involves memorizing extra formulas. If you use unit vectors you can't miss!
     
  4. Nov 12, 2013 #3
    thank you very much! that makes understanding the direction of the vectors simpler.

    for the second problem, I'd like some clarification on what your notation symbols represent. j represents the vector moving in the positive y-direction correct? and i is the magnetic field in the negative x-direction? Also, are P and H synonymous with the c and B vectors (as denoted in the figure) so c = E X B?

    thanks again!
     
  5. Nov 13, 2013 #4

    rude man

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    i, j and k are the unit vectors in the +x, +y and +z directions respectively.

    In your figure, B points in the -i direction and c points in the +j direction.
     
  6. Nov 13, 2013 #5

    rude man

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    j points, does not necessarily move, in the +y direction.

    And i points in the +x, not -x, direction.

    You should review how the unit vectors behave as you take cross-products of any two of them to get the third. For example, understand that i x -j = -k, k x -i = -j etc.
     
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