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.)

 

[asteriatic]

(I'm not sure which unit it is)

I would first like to commend the student for their attempt at solving the problem and using the correct equations. However, I would like to point out a few things:

1. In part a), the student has correctly used the equation for electric potential energy, but has made a mistake in the calculation. The correct answer should be 4.05 J (not -405 J).

2. In part b), the student has used the equation for electric potential, but has not taken into account the distance between the charges. The correct equation should be V=kq/r, where r is the distance between the charge and the point Z. Without knowing this distance, it is not possible to calculate the electric potential at point Z.

3. Additionally, in both parts a) and b), it is important to note that the electric potential energy and electric potential are scalar quantities and should not have units of J/C. The correct units for electric potential energy are J and for electric potential are V (volts).

Overall, the student has demonstrated a good understanding of the concepts and equations related to electric potential and potential energy, but there are some errors in the calculations. I would suggest reviewing the calculations and units to ensure accuracy in the future.