Three point charges are arranged on the line, what is the electric potential of the system?

Question

Three point charges are arranged on the line. Charge q₁=-5nC and is at x=-4cm, charge q₂=-3nC and is at x=4cm, charge q₃=+3nC and is at x=2cm. What is the electric potential energy of this system?

Answer 1

Student,

 

You are asking 2 different questions.  In the title, you ask for electric potential.  In the problem description, you ask for electric potential energy.  They are not the same thing.  I assume you really meant to ask the latter, since potential must be evaluated at a specified field point, and no field point is stated in the problem.  I will show you how to find total electric potential energy, but YOU do the calculations. 

 

The total electric potential energy is the sum of electric potential energies of all pairs of charges, without double-counting any pair.

 

U = U₁₂ + U₁₃ + U₂₃ = k(q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃)

 

q₁ = -5 x 10^-9 C

q₂ = -3 x 10^-9 C

q₃ = 3 x 10^-9 C

 

r₁₂ = |-0.04 - 0.04| m = ? m

r₁₃ = |-0.04 - 0.02| m = ? m

r₂₃ = |0.04 - 0.02| m = ? m

 

k = 9 x 10⁹ Nm²/C²

 

Plug in the numbers in the indicated units and with the correct signs for the charges, and get U in joules.