Question

1. You have an insulating sphere of radius ? with positive charge ? uniformly distributed throughout its volume.
   a) Calculate the electric field inside the sphere, as a function of ?, measured from the center.
   b) Now, you drill a tunnel of negligible radius from one pole of the sphere to the other. You hold

   an electron of mass ?Z and charge −? right at the tunnel opening and drop it in from rest,

   causing it to undergo simple harmonic motion! Calculate the angular frequency, ?.
   c) Find the oscillating system’s total energy. Note: There are multiple ways to do this, e.g. simple

   harmonic motion, electrostatic energy, work, etc. Pick your favorite method!

2. I only need help with b and c please

Answer 1

4) electric field al distance is : ( 762 consider gaussian Surface of sadius r. Eganz ging E(1792) in ar? JEST - Gato R3 This ) is the distance force at Force = (9XE ) = electric to 9=-e , E = Qr F:-ego These really hopes Re 47€ FORS" FE-kx Simple Harmonic . Motion. XER o . Then Angular frequency (c) landing = WEB m 46mR? This is the Angular frequency Total Energy = oscillating sim Energy + a Energy of insulating nere. scillating energoy :- LKA² here (Amplitud AER)

I Secood - Insulating sphere energy : for Volume charge energy is W = El E? de de=Volume element all space ? te le de inside Ei= gr outside. Lato R3 Eos lo - Anto J2 Warehouse to ] C 7? sino drdoda) Wurule = yes (a+sne drdodos 8 to Wrot = .02 . 2 Sote = 60 hoa GOR 8tto R. - - Tonto R - Now, The total energy = Wtot + Es