### Electrostatics Problem: Work Required for Four-Charge Configuration**Problem Statement:**How much work is required to set up the four-charge configuration of the figure if \( q = 6.60 \) pC, \( a = 79.9 \) cm, and the particles are initially infinitely far apart and at rest?**Options:**(a) \(-1.27 \times 10^{-12} \, \text{J}\) (b) \(-2.25 \times 10^{-12} \, \text{J}\) (c) \(-2.75 \times 10^{-12} \, \text{J}\) (d) \(-1.60 \times 10^{-12} \, \text{J}\) (e) None of the above **Diagram Explanation:**The figure depicts a square configuration with side length \(a\), where each vertex holds a point charge: - Top-left corner: \(+q\)- Top-right corner: \(-q\)- Bottom-right corner: \(+q\)- Bottom-left corner: \(-q\)The charges are placed such that opposite corners have the same charges. The distance between each adjacent pair of charges is \(a\).To calculate the work required to assemble this configuration:1. **Work to Bring First Charge:** Zero, since there is no electric field initially.2. **Work to Bring Second Charge:** \[ \frac{kq^2}{a} \]3. **Work to Bring Third Charge:** \[ -\frac{kq^2}{a} + \frac{kq^2}{\sqrt{2a}} \]4. **Work to Bring Fourth Charge:** \[ \frac{kq^2}{a} - \frac{kq^2}{a} + \frac{kq^2}{a} + \frac{kq^2}{\sqrt{2a}} \]Summing up all these values should give us the total work needed to arrange these charges. Calculate and then choose the appropriate option from the given choices.

Draw the energy diagram of the system.

How much work is required to set up the four-charge configuration of the figure if q = 6.60 pC, a = 79.9 cm, and the particles are initially infinitely far apart and at rest? %3D +q -4 +q (a) -1.27x10-12 J (b) -2.25x10-12 ] (c) -2.75x10-12 ] (d) -1.60x10-12 J (e) None of the above

How much work is required to set up the four-charge configuration of the figure if q = 6.60 pC, a = 79.9 cm, and the particles are initially infinitely far apart and at rest? %3D +q -4 +q (a) -1.27x10-12 J (b) -2.25x10-12 ] (c) -2.75x10-12 ] (d) -1.60x10-12 J (e) None of the above

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Electrostatics Problem: Work Required for Four-Charge Configuration

**Problem Statement:**
How much work is required to set up the four-charge configuration of the figure if \( q = 6.60 \) pC, \( a = 79.9 \) cm, and the particles are initially infinitely far apart and at rest?

**Options:**
(a) \(-1.27 \times 10^{-12} \, \text{J}\)
(b) \(-2.25 \times 10^{-12} \, \text{J}\)
(c) \(-2.75 \times 10^{-12} \, \text{J}\)
(d) \(-1.60 \times 10^{-12} \, \text{J}\)
(e) None of the above

**Diagram Explanation:**
The figure depicts a square configuration with side length \(a\), where each vertex holds a point charge:
- Top-left corner: \(+q\)
- Top-right corner: \(-q\)
- Bottom-right corner: \(+q\)
- Bottom-left corner: \(-q\)

The charges are placed such that opposite corners have the same charges. The distance between each adjacent pair of charges is \(a\).

To calculate the work required to assemble this configuration:

1. **Work to Bring First Charge:** Zero, since there is no electric field initially.
2. **Work to Bring Second Charge:**
\[
\frac{kq^2}{a}
\]
3. **Work to Bring Third Charge:**
\[
-\frac{kq^2}{a} + \frac{kq^2}{\sqrt{2a}}
\]
4. **Work to Bring Fourth Charge:**
\[
\frac{kq^2}{a} - \frac{kq^2}{a} + \frac{kq^2}{a} + \frac{kq^2}{\sqrt{2a}}
\]

Summing up all these values should give us the total work needed to arrange these charges.

Calculate and then choose the appropriate option from the given choices.

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