(Solved): (1) Suppose an electron (charge \( -e \) with \( e=1.6 \times 10^{-19} \mathrm{C} \) ) is located i ...

(1) Suppose an electron (charge \( -e \) with \( e=1.6 \times 10^{-19} \mathrm{C} \) ) is located inside a uniformly charged sphere with total charge \( +e \) and radius \( R=10^{-10} \mathrm{~m} \). Show that the force on the electron exerted by the positive charge is \[ \mathbf{F}=-\frac{e^{2} r}{4 \pi \epsilon_{0} R^{3}} \mathbf{e}_{r} \] (2) Applying Newton's 2nd law to the electron inside the sphere show that the electron undergoes an oscillating motion and find the corresponding angular frequency \( \omega \).