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Gogeta007

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**Magnetism and Inductance**

## Homework Statement

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:

x

^{2}+y

^{2}=a

_{0}

^{2}; 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)(x

^{2}+y

^{2}+z

^{2}) ] (xi

^{head}+yj

^{head}+ z

^{khead})

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:

F

_{av}=a

_{0}eB(sqr)[2/m(a

_{0}2+h2)][E+(e2/4pi epsilon a

_{0[/SUB)]khead Homework Equations Im not sure. . . I guess (int)B*dA = 0 Im completely lost and I don't know where or how to start The Attempt at a Solution Im completely lost. . .all I have is the drawing of an atom. Homework Statement You have 5 straight wires of length 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 Homework 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 don't know how to take in consideration the other 2 inductors and capacitors 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 I am loomking for but I can't 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 don't know how to get rid of that 2}

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