### Electric Potential at the Midpoint of an Isosceles Triangle#### Problem Statement:The three charges in the figure below are at the vertices of an isosceles triangle. Let \( q = 3.50 \text{ nC} \) and calculate the electric potential at the midpoint of the base. (Let \( d_1 = 2.50 \text{ cm} \) and \( d_2 = 6.50 \text{ cm} \)).#### Given:- Charge \( q = 3.50 \text{ nC} \)- Distance \( d_1 = 2.50 \text{ cm} \)- Distance \( d_2 = 6.50 \text{ cm} \)#### Diagram Explanation:The diagram depicts an isosceles triangle with three charges located at its vertices:- \( +q \) at the top vertex.- \( -q \) at the left base vertex.- \( -q \) at the right base vertex.The distances mentioned:- \( d_1 \), which is 2.50 cm, is the horizontal distance between the two negative charges at the base.- \( d_2 \), which is 6.50 cm, is the equal distance from the positive charge to each of the negative charges at the base.#### Task:Calculate the electric potential at the midpoint of the base of the triangle. Representation of the isosceles triangle with charges \( \pm q \) and distances \( d_1 \) and \( d_2 \).### Electric Potential Calculation:1. The electric potential \(V\) due to a point charge \(q\) at a distance \(r\) is given by:\[ V = \frac{kq}{r} \]where \( k \) is Coulomb's constant (\( k \approx 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).2. Contributions from each charge to the potential at the midpoint \(M\) of the base: - The midpoint of the base is equidistant from the two negative charges. - Distance from midpoint to each negative

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The three charges in the figure below are at the vertices of an isosceles triangle. Let q = 3.50 nC and calculate the electric potential at the midpoint of the base. (Let d₁ = 2.50 cm and d₂ = 6.50 cm.) kV

The three charges in the figure below are at the vertices of an isosceles triangle. Let q = 3.50 nC and calculate the electric potential at the midpoint of the base. (Let d₁ = 2.50 cm and d₂ = 6.50 cm.) kV

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 82P

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### Electric Potential at the Midpoint of an Isosceles Triangle

#### Problem Statement:
The three charges in the figure below are at the vertices of an isosceles triangle. Let \( q = 3.50 \text{ nC} \) and calculate the electric potential at the midpoint of the base. (Let \( d_1 = 2.50 \text{ cm} \) and \( d_2 = 6.50 \text{ cm} \)).

#### Given:
- Charge \( q = 3.50 \text{ nC} \)
- Distance \( d_1 = 2.50 \text{ cm} \)
- Distance \( d_2 = 6.50 \text{ cm} \)

#### Diagram Explanation:
The diagram depicts an isosceles triangle with three charges located at its vertices:
- \( +q \) at the top vertex.
- \( -q \) at the left base vertex.
- \( -q \) at the right base vertex.

The distances mentioned:
- \( d_1 \), which is 2.50 cm, is the horizontal distance between the two negative charges at the base.
- \( d_2 \), which is 6.50 cm, is the equal distance from the positive charge to each of the negative charges at the base.

#### Task:
Calculate the electric potential at the midpoint of the base of the triangle.

<div>
<img src="image_url_here.jpg" alt="Isosceles triangle with charges" style="width:40%;"/>
<p>Representation of the isosceles triangle with charges \( \pm q \) and distances \( d_1 \) and \( d_2 \).</p>
</div>

### Electric Potential Calculation:

1. The electric potential \(V\) due to a point charge \(q\) at a distance \(r\) is given by:
\[ V = \frac{kq}{r} \]
where \( k \) is Coulomb's constant (\( k \approx 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).

2. Contributions from each charge to the potential at the midpoint \(M\) of the base:
- The midpoint of the base is equidistant from the two negative charges.
- Distance from midpoint to each negative

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