Electric Potential Energy of a Charge Distribution

[HarleyM]

Homework Statement

Examine the diagram provided,
Sphere 1: q=3.0x10^-4C
Sphere 2: q=-3.0x10^-4C
Sphere 3: q= 3x10^-4C

a) Find the total electric potential energy of the charge distribution
b) Find the total electric potential at point Z

Homework Equations

E_E=kq₁q₂/r +kq₂q₃/r+kq₁+q₃/r... etc

V=kq/r

The Attempt at a Solution

a) E_E= kq₁q₂/r +kq₂q₃/r+kq₁+q₃/r
E_E=(9x10⁹)[(3.0x10^-4*(-3.0x10^-4)/3) + ((-3.0x10^-4*(3.0x10^-4)/3) + ((3.0x10^-4*3.0x10^-4)/6)]
E_E= -405 J (Does anyone else get the same answer? I tried to do it continuously in my calculator so I don't lose digits)

b) V= K(q₁/r+q₂/r+q₃/r)
V=(9x10⁹)[(3.0x10^-4/4.24)+(-3.0x10^-4/3)+(3.0x10^-4/4.24)]

V=3.7x10⁵ V or J/C

 

[SammyS]

Those answers look good to me.

 

[HarleyM]

Ok thanks!

 

[ch_advanced]

Those are tough to calculate all at once. It took me a few tries but I did end up with the same answers.
For anyone else who likes to take things one step at a time, here you go:

a) E = k[(-3x10^-8)+(1.5x10^-8)+(-3x10^-8)]

b) V = k(4.15094x10^-5)

(and at the end, when your multiplying the final sum by Coulomb's Constant (k=9x10^9), make sure to put brackets around that too. Seems to make a difference.)