**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

Answered: Image /qna-images/answer/ba146282-1e0d-4c2e-a08e-5027ed519511.jpg

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)...

See similar textbooks

Related questions

Q: What is the electric potential, in volts, due to the proton on an electron in an orbit with radius…

Q: What will be the electric potential at a distance of 0.15 m from a point charge of 6.0 uC? Group of…

Q: A fixed point charge of 3 nC is located at the origin of a Cartesian coordinate system. The charge…

Q: A rubber sheet of infinite size has an area charge density of σ = -48.5 nC/m^2 spread uniformly on…

A: Given:- The electric field is given by the rubber sheet and glass fiber with line…

Q: The figure shows three circular, nonconducting arcs of radius R = 8.04 cm. The charges on the arcs…

Q: The figure shows a thin plastic rod of length L = 15.9 cm and uniform positive charge Q=51.5 fC…

Q: What is the electric potential V due to the nucleus of hydrogen at a distance of 5.292 × 10-¹¹ m?…

A: According to the question data provided Distance =r = 5.292x10-11 m As we know that hydrogen nucleus…

Q: A uniformly charged insulating rod of length 16.0 cm is bent into the shape of a semicircle as shown…

A: The length of the rod,

Q: A spherical conductor has a radius of 14 cm and a charge of 20 µc. Calculate the electric field and…

A: In any conducting body like cylinder and shell the charge exist only on the surface of the body. At…

Q: y 11. Three charges +Q, -Q and -Q are located on the circumference of a circle of radius r as shown.…

A: Step 1: Step 2: Step 3: Step 4:

Q: semicircle as shown in the figure below. The rod has a total charge of -6.00 µC. Find the electric…

Q: Two charges of equal magnitude but opposite sign, q1 = 40 nC and q2 = -40 nC, are separated by a…

Q: A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point…

A: Given: The charge that is distributed on the isolated spherical conductor: q = 40 pC; The radius of…

Q: Three point charges, Qi 15.4 µC, Q2 = -30.6 µC, and Q3 = 57.3 µC, are arranged as shown in the…

A: Given data:

Q: A rubber sheet of infinite size has an area charge density of σ = -66.3 nC/m^2 spread uniformly on…

A: Electric potential difference at a half-way point between the sheet and the glass fiber due to the…

Q: three point charges, -5.6E-9 C, -8.7E-9 C, and 6.2E-9 C, are fixed at a different position on a…

A: Here r=−1600−72.9=0.0455≃0.046m.

Q: Three concentric conducting spherical shells of radii r, 2r, and 3r are charged with net electric…

Q: Find an expression for Electric Potential differences formed by a semicircle charged rod with a…

A: The total charge in the semi circular rod is Q=50μC = 50×10-6 C. The radius of the rod is R = 30.0…

Q: A total electric charge of 4.50 nC is distributed uniformly over the surface of a metal sphere with…

A: Given data, Charge Q=4.5 nC = 4.5×10-9 C. Radius of sphere R=26 cm = 26×10-2 m.

Q: A charge Q=-13 nC is placed at the origin. What is the electric potential at point A=(4.2, -4.7) cm?…

Q: Three point charges, Q1 = 18.4 µC, Q2 = -33.6 µC, and Q3 = 67.3 µC, are arranged as shown in the…

Q: a uniform electric is indicated by electric line. the electric magnitude is 150 n/c. if the object…

A: Given that electric field E = 150 N/C d = 0.25m

Q: R= 30 cm OP- 40 cm D.

Q: Chapter 25 Q178: Three circular, nonconducting arcs of radius R = 3 cm.The charges on the arcs are…

Q: - 22.4 μC , Q-38.6 μC, and Q3 = 57.3 µC, are arranged as shown in the figure. The Three point…

A: Given, Q1 = 22.4 μCQ2 = -38.6 μCQ3 = 57.3 μCx = y = 50.1 cm = 0.501 m

Concept explainers

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

100%

**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: 5

2. **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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

What is the magnitude of an electric field at the point (3.00 i – 2.00 j + 4.00 k) m, if the electric potential is given by ? b V=2xyz^2
A uniform electric field of magnitude 336 V/m is directed in the positive x-direction. Suppose a 19 µC charge moves from the origin to point A at the coordinates, (20 cm, 53 cm). What is the absolute value of the change in potential from the origin to point A? Answer in units of V.
A long cylindrical insulating shell has an inner radius of a=1.41 m and an outer radius of b=1.6 m. The shell has a constant charge density of 3.5×10−9 C/m3. The picture shows an end-on cross-section of the cylindrical shell. If we take the potential at the axis to be zero, what is the electric potential at the outer radius of the shell?
A point charge of 1 μC is located at the origin, which is the center of a thin spherical shell of 10 cm radius. This shell is uniformly charged with 17 μC. What is the electric field at r=5 cm and r=15?E1 = V/m,E2= V/m.What is the electric potential at these points?V1 = V,V2= V.
Needs Complete typed solution with 100 % accuracy.
Identical 12μC charges are placed at the ends of a metre stick. 12 μC 12 JC P What is the electric potential at point P at the 60 cm mark on the metre stick? Enter your answer
Answer the question
In the figure a plastic rod having a uniformly distributed charge Q = -27.2 pC has been bent into a circular arc of radius 1.82 cm and central angle 120°. With V = 0 at infinity, what is the electric potential in volts at P, the center of curvature of the rod? Number i Units + Q
A spherical conductor whose center is at point O and radius R = 20 cm, is given a charge Q = + 100 μC a. Calculate the electric potential at points A and B if the distance OA = 30 cm and the distance OB = 45 cm. b. How much work is required to move an electron from point A to point B?
Two charged particles create an electric potential, and everywhere in the xy-plane this potential is described by the following function. 32.0 V 50.0 V √(x + 1.18 m)² + y² x² + (y - 2.30 m)² Determine the charge and coordinates for the position of the two particles. Give the charge (in nC) and coordinates (in m) for the position of the particle responsible for the first term first. first term 91 = X = 92 = V = y = Give the charge (in nC) and coordinates (in m) for the position of the particle responsible for the second term. X = y = nC m m nC 3 3 8 m
A positive charge is evenly distributed on the surface of a metal sphere centered at the origin of the coordinate system. The positive charge produces an electric field that points outwardly in the radial direction. A positive test charge is fixed at a distance R₁ from the center of the coordinate system, far from the surface of the sphere. The electric potential at R₁ is 10V. The positive test charge is then allowed to move freely until it reaches a distance R₂=2R₁ from the center of the coordinate system. What is the electric potential (in Volts) of the test charge at its new resting point? 10
B A A 6 µC point charge is placed at the origin as shown in the figure above, where a = 2 cm, 6 = 2.4 cm, c = 1 cm, and d = 2.7 cm. Find the potential at the points A, B and C: VA V VB = V Vc = V