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Homework Help: Properties of electric lines of force

  1. Jul 2, 2011 #1
    1. The problem statement, all variables and given/known data

    my textbook mentions the following as properties of lines of forces among other things
    They do not pass through a conductor.

    They contract longitudinally.

    They exert a lateral pressure on each other.
    I want clarification on these points
    i) Why lines of force do not pass through the conductor?
    What is meant by exerting lateral pressure among each other and contracting longitudinally?
    Thanks in advance revered members

    2. Relevant equations

    3. The attempt at a solution
    I think lines of force represent path taken by the charge, then how can we say that they don't pass through the conductor
  2. jcsd
  3. Jul 2, 2011 #2

    Philip Wood

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    Gold Member

    Start with a definition of a line of force. It is a line (straight or curved) whose direction (or, if you prefer, the direction of whose tangent) at any point along it is the direction of the electric field strength vector, E, at that point.

    This is not, in general, the same as the path a free charge would take. [A free charge would pick up speed and would 'go wide' on bends.]

    Now, about inside a conductor... You're clearly studying the electrostatic case. What must be the electric field strength inside a conductor if its free electrons aren't drifting? Can you see how this solves your problem?

    Now what about lateral pressure and longitudinal contraction? Well, draw the pattern of lines of force between a small positive charge and a small negative charge. [You do this by vector addition of the fields due to each charge separately, to establish the resultant field direction at a number of points - enough to see what the pattern of lines is going to be.]

    Faraday imagined these lines of force as real things, elbowing each other apart, and also under tension, pulling the charges together. If your teacher favours this conception, go along with it. But don't forget that the definition I gave at the beginning is the bedrock.
  4. Jul 4, 2011 #3
    i understood about lines of force not travelling inside the conductor. but i can't understand lateral pressure and longitudinal contraction,sir? could u elaborate? also thanks for the reply.
  5. Jul 4, 2011 #4

    Philip Wood

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    Gold Member

    Did you manage to sketch the lines of force due to two separated equal and opposite charges? If not you could cheat by googling 'dipole field' and finding an image: makes sure it's an electric dipole rather than a magnetic dipole.

    Can you now see from the image why Faraday thought of the lines as elbowing each other apart, and as under tension and pulling together the charges which they join? Physicists don't now regard lines of force as explaining in this way how charges attract each other. It was, though, a hugely important idea, because it suggested that to understand the forces exerted by charges on one another, one needed to consider things going on in the space between the charges.

    You should carefully distinguish Faraday's speculative view of lines of force pushing sideways but under tension from the 'hard facts' about lines of force, which can be deduced from their definition and the laws of electromagnetism. For example, pattern of lines of force due to a dipole can be drawn by vectorially adding the fields (given by the inverse square law) for the individual charges, at a number of points. It is also clear from the definition that lines of force can't cross. The dipole field also illustrates the property of lines of force that the closer together they come the stronger the field.

    The Faraday picture (lines pushing apart and under tension) is not among these 'hard facts'. In my view, not using it will not harm your understanding of electric fields.
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