https://r2.erweima.ai/mathbot/image/1726438673347gr5be1cf.jpg

The image contains two parts related to the electrostatic potential, asking to plot potential functions along the x-axis for given intervals and conditions. Let me break it down:

### Part a)
You are asked to **plot the electrostatic potential along the x-axis** for a specific interval:
\[
-3a < x < 3a
\]
This graph should use units of potential in terms of \( \frac{kQ}{a} \), where:
- \( k \) is the Coulomb constant.
- \( Q \) is the charge.
- \( a \) is a characteristic distance.

The potential function for a point charge located on the y-axis at \( y = 0 \) (since no position for the charge is given) will follow the formula for the potential due to a point charge:
\[
V(x) = \frac{kQ}{r} = \frac{kQ}{\sqrt{x^2 + y^2}}
\]
Assuming \( y = 0 \), this simplifies to:
\[
V(x) = \frac{kQ}{|x|}
\]

So, you would need to plot \( V(x) = \frac{kQ}{|x|} \) for the interval from \( -3a \) to \( 3a \), showing symmetry around the origin.

### Part b)
Now, the problem adds a negative charge placed at \( y = -a \). The task is to plot the potential along the x-axis in the interval:
\[
-4a < x < 4a
\]
The potential function for a point charge at position \( (0, -a) \) will be:
\[
V(x) = \frac{kQ}{r} = \frac{-kQ}{\sqrt{x^2 + a^2}}
\]
Here, the charge is negative, which changes the sign of the potential.

To solve this, plot the function \( V(x) = \frac{-kQ}{\sqrt{x^2 + a^2}} \) for the interval \( -4a < x < 4a \), taking into account that the potential is negative.

### Next Steps
Would you like me to create these graphs or provide any more detailed steps or clarifications on how to proceed?

Trace una gráfica del potencial en puntos a lo largo del eje de las x en el intervalo -3a < x < 3a en unidades de kQ/a. Permita que la carga localizada en y = -a sea negativa y trace el potencial a lo largo del eje de las x en el intervalo -4a < x < 4a.

Learn how to graph the electrostatic potential along the x-axis for different charge configurations. Part (a) covers a point charge on the axis, and part (b) includes a negative charge located at y = -a. The potential is calculated using Coulomb's Law and is expressed in units of kQ/a.

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