Two negative particles of charge=-Q and mass=rn orbits a stationary, positive particle of charge=+2Q at a radius= R' They are always at diametrically opposite points on the orbit.

Question

a.
Find the total inward Coulomb force on one negative particle.
b.
Write the equation that total Coulomb force provides the centripetal force.
c.
Use (b.) to write the kinetic energy in terms of Q, R' but not velocity.

d.
Find a formula for the total energy for three Coulomb interactions and two
orbiting particles in terms of Q and R but not velocity.
e.
Work=W is done to remove one negative particle to infinite distance,
leaving one negative particle orbiting the +2Q particle at a radius of R, .
Write that the Coulomb force provides the centripetal force and use this
equation to find an expression for the total energy (KE+PE) of the nonneutral
system.
f Write that the work=W provides the difference in energy between (d.) and
(e.)
g.
Use (f.) to express the radius Rf in terms ofW, Q, Ro ' etc.
h.
In the Helium atom, two electrons orbit an alpha particle (two protons and two neutrons) at a radius of Ro = 31_ pm . Express this in meters. The
first ionization energy for (He ~ He+ + e-) is W= 24.6 eV. Express this
in Joules.
i. Use (g.) and (h.) to find the radius of the He+ ion, Rf•
j.
Use (e.) and (i.) to find the second ionization energy, the work needed to
remove the last electron. This is the total energy of the ion.
k.
Express (j.) in electron volts.
Question 2
2. Inside a sphere of radius R, charge is distributed with density, p =wrg • Outside the sphere, there is NO charge. The constants, wand g, are positive.
a.
Carefully find the charge enclosed by a concentric sphere of radius r<R.
b.
Use Gauss' Law to find the electric field inside the sphere at radius r.
c.
Write an expression for the voltage, V=V(r ) inside the sphere.
d.
Find the electric field outside the sphere.
e.
Find the voltage, V=V(r) outside the sphere.
f.
Match (c.) and (e.) at r=R to find the constant in (c.).
g.
What is the voltage at the center, where r=O?

Answer 1

So did you try them? Do you really think I am going to just do them both for you? I am getting sleepy and have not done these since 1957. Show your attempt and maybe some other physicist will come along and see if you are on the right path. They are not hard, but they will take a while and be careful about signs and for example for the very first one you will calculate the attraction force on one -Q due to the +2Q at the center but do not forget the opposite much smaller repelling force due to the other negative charge on the opposite side. I do not know why they used +2Q and -Q and -Q instead of going straight to the Helium atom which is what they are getting at.