What is the potential energy of the fifth particle

Question

Assignment:

Problems:

1. The electric potential at a point on the axis of a ring of charge of radius R=3 m is

V= (1/4πε₀) - (Q/√Z² + R²)

Q = 125 nC. If a point charge q =  15 nC is located at z = 4 m, find the net force exerted on the charged particle by the ring.

2. A thin, uniformly charged rod of length L = 4.0 m with a linear charge density λ. = 1/9 nC/m lies along the x-axis as shown below. Find the electric potential difference at point P a distance d = 3 m from the origin.

3. Four charged particles at the corners of a rectangle is shown below. If a fifth charged particle with Q = 4C is carried from infinity and placed at point the center of the rectangle, what is the potential energy of the fifth particle?

4. Point P in the figure shown below is a distance d₁ = 4.00 m from Q₁ (Q₁= -2e) and a distance d₂ = 2.00 m from Q₂ (Q₂= +2e) with both Q₁ and Q₂ fixed in place.

(a) With V = 0 at infinity, what is Vat point P?

(b) If we bring a particular charge (Q₃ (Q₃= +2e) from infinity to point P, how much work do we do?

(c) What is the potential energy of the three-particle system?