Electrical Potential Energy and Electric Potential

Question

Please do provide an in-depth step-by-step solution and a final answer on how you solved it... This is my very first time encountering these problems. Thank you so much, in advance.!

1. Two charges, 𝑞1=1.3𝜇𝐶 and 𝑞2=4.7𝑛𝐶 has a potential energy of 2.34×10−7𝐽.Find the distance between the two charges.
2. Two charges, 𝑞1=−3𝜇𝐶 and 𝑞2=−5𝜇𝐶 are separated by a distance of 6.0𝑚. Suppose that 𝑞1 is 6 meters to the right of 𝑞2.What is the electric potential at point A where point A is 2.5 meters to the left of 𝑞1?Draw an illustration of the two charges and point A.

Answer 1

1) I will show you the equations that apply. I will leave the algebra and solution to you. The peotential energy between two point charges is U_e = k_eQ₁Q₂/d with ke = 8.99 x 10⁹ N-m²/C² , Qs are charges in Coulombs, d is in meters, and U is the electrical potential energy in Joules. Here you isolate d algebraically and substitute with the appropriate units. (Note μC = 10^-6 C and nC = 10^-9C)

2) So the situation is that q₂ is to the left, A is 3.5 m to the right of it, and q₃ is 6 meters to the right of it.

Potential energy is a scalar which means that you can plug into the V formula for each: V_i = k_eq_i/d_i for i = 1,2 and the answers will be in volts( Note that the sign of q being negative makes V negative and that d₁=3.5 m and d₂ = 2.5 m