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Loop of electron

  1. Dec 6, 2009 #1
    Magnetism and Inductance

    1. The problem statement, all variables and given/known data
    Consider th eloop model of an electron's orbig in a hydrogen atom. The electron has mass me and charge -e. The path of the loop is given by the following two equations:
    x2+y2=a02; z=h
    Ignoring special relativistic effects, pretend that the total energy E of the electron is due only to two phenomena: its kinetic energy associated with the loop and its electrostatic potential energy associated with the proton. You have a magnetic field,

    (vector)B=B/ [ (sqr)(x2+y2+z2) ] (xihead +yjhead + zkhead)

    which produces a net upward magnetic force on the loop.
    (a) when viewed from the origin, is the lectron moving clockwise or counterclockwise?
    (b) show that the average force on the loop due to B is given by:

    Fav=a0eB(sqr)[2/m(a02+h2)][E+(e2/4pi epsilon a0[/SUB)]khead

    2. Relevant equations

    Im not sure. . .
    I guess (int)B*dA = 0
    Im completely lost and I dont know where or how to start

    3. The attempt at a solution

    Im completely lost. . .all I have is the drawing of an atom.







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

    You have 5 straight wires of lenght l=2 in the xy plane, four of which make a square centered at th eorigin with sides parallel to the axes of the coordinate system. The fifth wire bisects the square along the y axis. You now insert three inductors and two capacitors to make a special LC circuit. The inductors are located along the x axis at x=-1,0,+1 and each has inductance L. The capacitors are located along the line y-1 at x values of +1/2 -1/2 and each has capacitance C.
    (a) if the currents in the left and right side inductorsa re in the j and -j directions, respecitively and both equal (i(t) show that the angular frequency of the oscillating current is given by:
    (omega)=1/(sqr)LC

    (b) If the direction of the current in the right side inductor is reversed show that the angular reqluency of the oscillating current is given by:

    (omega)=1/(sqr)3LC

    2. Relevant equations

    I am able to do (and get the first equation) but only with a simple LC circuit (one capacitor and one inductor

    knowing that Vc=VL
    Vc=q/C = L di/dt
    take a time derivative
    dq/Cdt = L d2i/dt2

    solve and get a second order linear homogeneous eq.

    and to arrange and get omega you need to equal omega to 1/(sqr)LC

    but I dont know how to take in consideration the other 2 inductors and capacitors

    3. The attempt at a solution

    Im thinking you have to add the capacitors sinec they are in series and the inductors that are in parallel, but trying this didnt yield anything.
    i tried

    2Vc=3VL
    but didnt get anywhere either, I got the 3 coefficient that im loomking for but I cant cancel that 2.

    I have this:

    energy total should be the addition of all components
    so
    energy for a capacitor: q2/2C
    energy for an inductor: (LI2)/2

    UT=2UC+3UL=

    2C + 3L = 0
    q2/C = - 3(Ld2q/dt2)/2

    <. . . stuff. . .>

    I get 2/(sqr)3LC

    I dont know how to get rid of that 2
     
    Last edited: Dec 6, 2009
  2. jcsd
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