The problem involves multiple point charges and a line charge distributed uniformly, and asks for the potential $V$ at a certain point. Let's break down the problem.

Problem Breakdown:

1. Point charges:

   • Charge 1: $50 \, \text{nC}$ located at $(3, 4, 0)$
   • Charge 2: $x \, \text{nC}$ located at $(4, 2, -3)$
   • Charge 3: $(2, -6, 5)$, the charge is unspecified but it appears to be part of the setup.

2. Line charge:

   • A line along $x = 3$, $y = -4$, with a uniform charge density of $55 \, \text{nC/m}$.

3. Potential given:

   • $V = 0 \, \text{V}$ at $O(0, 0, 0)$.

4. We are asked to find:

   • The potential at point $A$ at $(y, y, 5)$.

Potential Due to Point Charges

The potential $V$ at a point due to a point charge $q$ located at a distance $r$ from the point is given by the formula: $V = \frac{kq}{r}$ where $k = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2$ is Coulomb's constant, and $r$ is the distance between the charge and the point of interest.

We will need to compute the distance between the given point charges and the point $A$, and sum up the contributions from each charge.

Potential Due to the Line Charge

For a line charge, the potential at a point a distance $r$ from the line is: $V_{\text{line}} = \frac{\lambda}{2\pi \epsilon_0} \ln\left(\frac{r_0}{r}\right)$ where:

• $\lambda = 55 \, \text{nC/m}$ is the linear charge density,
• $\epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}$,
• $r$ is the perpendicular distance from the point to the line.

Let me calculate the potential at the given point $A(y, y, 5)$ considering the contributions of the point charges and the line charge.Here are the results for the contributions to the potential at point $A(3, 3, 5)$:

1. Potential due to the first point charge (50 nC at $(3, 4, 0)$): $V_1 = 88.25 \, \text{V}$

2. Distance from point $A$ to the line charge located along $x = 3$ and $y = -4$ is $7 \, \text{m}$.

3. Potential due to the line charge with uniform charge density $55 \, \text{nC/m}$: $V_{\text{line}} = -1924.70 \, \text{V}$

Next, we would need the unknown charges and then sum the contributions to find the total potential at point $A$. Let me know if you'd like to proceed with assumptions for the missing charges or if you'd like to explore any part in more detail.

Here are some relative questions you might explore:

1. How would the potential change if the second point charge were given?
2. Can we assume symmetry or make approximations to estimate the missing charge?
3. How does the distance from the line charge affect the potential in general?
4. What is the significance of $V = 0$ at $O(0,0,0)$ in terms of reference potential?
5. How would we calculate the potential at a different point from these same charges?

Tip: Always remember to consider both point charges and continuous charge distributions (like line or surface charges) when calculating potentials.