1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Picture of electro-magnetic vector potential in 1+1 dimension spacetime?

  1. Feb 2, 2013 #1
    "Picture" of electro-magnetic vector potential in 1+1 dimension spacetime?

    I'm trying to model the electro-magnetic vector potential, does the following come close for 1 + 1 dimension spacetime? See sketches below.

    Consider an elastic string, under tension, between two fixed points A and B that lie on the z axis. Let the distance between points A and B be large. Let the motion of the string in the x and y directions be given by ψ_x(z,t) and ψ_y(z,t). The string is such that both ψ_x(z,t) and ψ_y(z,t) satisfy the wave equation ψ(z,t),tt = c^2ψ(z,t),zz.

    Now confine the motion of the string so that it moves freely on the surface of a cylinder of radius r, see below. Now let the position of the string be given by θ(z,t), with θ(A,t) and θ(B,t) = 0, and let θ(z,t) = 0 when the string is at rest. Define an orientation on the cylinder so we know which direction positive θ is.

    Now let charge density ρ(z,t) interact with the constrained string above in the following way, where ever we have positive (negative) charge density there is a perpendicular force on the string in the positive (negative) θ direction. The magnitude of the force in the θ direction on a segment of the string from z to z + dz is proportional to the charge density at z times dz. See below.

    The 1 + 1 dimensional vector potential A_0 will go like θ. the electric field will go like θ,z and A_z will go like θ times the velocity of the charge?

    Let there be two separated and localized charge densities, positive and negative, that act on the string in the manner above, see below.

    I think the 3 + 1 dimensional version of the above follows in a straight forward way.

    Thanks for any help or suggestions!

    Attached Files:

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Picture of electro-magnetic vector potential in 1+1 dimension spacetime?