**Title: Calculating the Electric Potential at the Center of a Circle with Symmetrically Placed Charges****Problem:**Five particles with equal negative charges \(2q\) are placed symmetrically around a circle of radius \(R\). Calculate the electric potential at the center of the circle.**Solution:**In this scenario, we have five particles each with a charge \(2q\) placed at equal distances on a circle with radius \(R\). We need to find the electric potential at the center of the circle due to these five charges.*Step-by-Step Solution:*1. **Identify the Known Values:** - Charge of each particle: \(2q\) - Radius of the circle: \(R\) - Number of charges: 52. **Symmetrical Placement:** Since the particles are placed symmetrically, they form a regular pentagon. 3. **Electric Potential Due to a Single Charge:** The electric potential \(V\) at a distance \(R\) from a charge \(2q\) is given by: \[ V = \frac{k \cdot 2q}{R} \] where \(k\) is Coulomb's constant (\(k = 8.99 \times 10^9 \frac{N \cdot m^2}{C^2}\)).4. **Superposition Principle:** In a configuration with multiple charges, the total electric potential at a point is the algebraic sum of the potentials due to the individual charges. Since electric potential is a scalar quantity, we can simply add the potentials from each of the five charges.5. **Calculate Total Electric Potential:** Since all charges are identical and equidistant from the center, the total electric potential \(V_{total}\) at the center of the circle is: \[ V_{total} = 5 \times \frac{k \cdot 2q}{R} = \frac{10kq}{R} \] **Conclusion:**The electric potential at the center of the circle due to the five symmetrically placed particles with charges \(2q\) is: \[ V_{total} = \frac{10kq}{R} \]This approach uses the principle of superposition and the formula for electric potential due to a point charge

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Answered: Five particles with equal negative…

Five particles with equal negative charges 2q are placed symmetrically around a circle of radius R. Calculate the electric potential at the center of the circle.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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