https://file.aiquickdraw.com/mathbot/file/1731004831340u2af4tkt.jpg

To determine the work done in placing a charge at the midpoint between two other charges, let's go through the necessary steps.

### Given Data:
1. \( q = 25.1 \, \mu C = 25.1 \times 10^{-6} \, C \) (charge placed at midpoint)
2. \( q_1 = q_2 = 7.8 \, nC = 7.8 \times 10^{-9} \, C \) (charges on either side of midpoint)
3. Distance between charges \( d = 50.6 \, mm = 0.0506 \, m \)
   - Therefore, each \( q_1 \) and \( q_2 \) are \( \frac{d}{2} = 0.0253 \, m \) from the midpoint.

### Formula
The work done in bringing a charge \( q \) to the midpoint is given by the electric potential at that point due to both charges, multiplied by \( q \):
\[
W = V \times q
\]
where \( V \) is the electric potential at the midpoint due to both charges \( q_1 \) and \( q_2 \).

The potential \( V \) at the midpoint due to a single charge \( q_1 \) located at distance \( r \) is:
\[
V = \frac{k \cdot q_1}{r}
\]
Since we have two charges \( q_1 \) and \( q_2 \) at the same distance from the midpoint, the total potential \( V_{total} \) is:
\[
V_{total} = \frac{k \cdot q_1}{r} + \frac{k \cdot q_2}{r} = \frac{2 \cdot k \cdot q_1}{r}
\]
where \( k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \).

### Calculation

1. **Calculate \( V_{total} \):**
   \[
   V_{total} = \frac{2 \cdot (8.99 \times 10^9) \cdot (7.8 \times 10^{-9})}{0.0253}
   \]

2. **Calculate Work \( W \):**
   \[
   W = V_{total} \times q
   \]
   Substitute \( q = 25.1 \times 10^{-6} \, C \).

After calculating, I will provide the answer in millijoules (mJ) rounded to one decimal place. Let’s proceed with the calculations.The work done in setting a 25.1 µC charge at the midpoint between the two 7.8 nC charges separated by 50.6 mm is **139.1 mJ**.

Would you like a detailed breakdown of the calculations or have any questions?

Here are some related questions for further exploration:
1. How would the work change if the distance between the charges were doubled?
2. What would be the work done if the midpoint charge had a different value?
3. How does the concept of electric potential energy relate to this problem?
4. What if the charges were of opposite signs—how would the calculation change?
5. How can this concept be applied to understand potential energy in electric fields?

**Tip:** Remember that the electric potential at a point is scalar, so potentials due to multiple charges add up without direction considerations.

How much work is done when you set a 25.1 µC charge at the midpoint between two 7.8 nC charges separated by a distance 50.6 mm? (please provide your answer in mJ to 1 decimal place)

Determine the work done in setting a 25.1 µC charge at the midpoint between two 7.8 nC charges separated by 50.6 mm. Learn the calculation process for electric potential and work in electrostatic fields, suitable for college-level physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation