4. Consider two conducting spheres with radii R, and R2 separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a minimum value, the potential difference between the spheres is zero. The total charge Q is equal to q, + 92, where q, represents the charge on the first sphere and q2 the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface. (a) Show that the energy associated with a single conducting sphere of radius R and charge Q surrounded by a vacuum is Ug = k.q²/2R . (b) Find the total energy of the system of two spheres in terms of q1, the total charge Q, and the radii R, and R2. (c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the derivative equal to zero. Solve for q, in terms of Q and the radii.

4. Consider two conducting spheres with radii R, and R2 separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a minimum value, the potential difference between the spheres is zero. The total charge Q is equal to q, + 92, where q, represents the charge on the first sphere and q2 the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface. (a) Show that the energy associated with a single conducting sphere of radius R and charge Q surrounded by a vacuum is Ug = k.q²/2R . (b) Find the total energy of the system of two spheres in terms of q1, the total charge Q, and the radii R, and R2. (c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the derivative equal to zero. Solve for q, in terms of Q and the radii.

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: 6. Three point-like charges are placed at the corners of a square as shown in the figure, 46.0 cm on…

A: Given q1=-1.20 μC =1.20×10-6 Cq2=2.60 μC =2.60×10-6 Cq3=3.60 μC =3.60×10-6 CDistance between two…

Q: 1. In a particular region, the electric potential is given by V=-xyz + 4xy What is the electric…

Q: A point charge q₁ = 85.7 μC is held fixed at the origin. A second point charge, with mass m =…

Q: A metal sphere (in electrostatic equilibrium) carries an excess positive charge. Location A is at…

Q: In the diagram, how much work is done by the electric field as a third charge q3 = +2.70 nC is moved…

Q: A proton (mass 1.67 x 10-27 kg, charge 1,60 x 10-19 C) moves from point A to point B under the…

A: Given data: Charge, q = 1.60 ×10-19 C Mass, m= 1.67 ×10-27 Kg speed at point B vB= 97.4 Km/s = 97400…

Q: Two positive point charges are 5.00 cm apart. ▼ Part A If the electric potential energy is 75.0 J,…

A: Given Distance between two point charges r = 5.00 cm = 0.05 m Electric potential energy U…

Q: 12. Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated…

Q: n the diagram, how much work is done by the electric field as a third charge q3 = +5.40 nC is mov…

A: Given:- The charge q1 = +8.30 nC and q2 = -8.30 nC The distance between the charge q1 and b is…

Q: Face area of 4.70 × and has a dielectric nside surface If the

A: Given: Dielectric constant(k)=4.5 thickness, d=1.5×10-8 m Surface area,A=5.25×10-9 m2 Change in…

Q: Consider a positive charge Q₁ of magnitude 9 µC fixed at the origin with another positive charge Q₂…

Q: Use the definition of potential difference in terms of electric field to deduce the formula for…

A: Given: r refers to the spherical radial coordinate Let , Va be the Potential of charge at point A…

Q: 4. Three point-like charges are placed at the corners of a square as shown in the figure, 30.0 cm on…

A: Magnitude of charge q1 =Magnitude of charge q2= Magnitude of charge q3 = Side of cube = 30 cm =…

Q: Cathode ray tubes (CRTS) used in old-style televisions have been replaced by modern LCD and LED…

A: Given data: Distance between plates (d) = 1.52 cm Potential difference (ΔV) = 28.0 kV Required: The…

Q: 1.Dry air will break down if the electric field exceeds about 3.0×10^6V/m. What amount of charge…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: A charge of -8.4 nC is uniformly distributed around a thin plastic ring lying in a yz plane with the…

Q: 6. A uniform electric field points in the negative x-direction, as shown. The magnitude of the…

A: Given, E= 1.0×104 N/C

Q: 1. What is a correct expression for the potential energy of the charge configuration illustrated…

A: The potential energy of the three charges q1, q2, q3 is given by Where k = Coulomb's constant…

Q: D1-RT60: UNIFORM ELECTRIC FIELD-POTENTIAL DIFFEREN Two parallel plates that have been charged create…

A: Given Data: The magnitude of uniform electric field E=30 NC Coordinates of point M (2,0) m…

Q: 14. The plates of a parallel-plate capacitor are 4.50 mm apart, and each carries a charge of…

Q: Four point charges, which are initially infinitely far apart, are placed on the four corners of a…

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

4. Consider two conducting spheres with radii R, and R2 separated by a
distance much greater than either radius. A total charge Q is shared
between the spheres. We wish to show that when the electric potential
energy of the system has a minimum value, the potential difference
between the spheres is zero. The total charge Q is equal to q, + 92,
where q, represents the charge on the first sphere and q2 the charge on
the second. Because the spheres are very far apart, you can assume the charge of each
is uniformly distributed over its surface.
(a) Show that the energy associated with a single conducting sphere of radius R and charge
Q surrounded by a vacuum is Ug = k.q²/2R .
(b) Find the total energy of the system of two spheres in terms of q1, the total charge Q, and
the radii R, and R2.
(c) To minimize the energy, differentiate the result to part (b) with respect to q, and set the
derivative equal to zero. Solve for q, in terms of Q and the radii.

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 8 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

Attached question and diagram.
5. A uniform electric field of magnitude 250 V/m is directed in the positive x direction. A 112.0-µC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change in the potential energy of the charge-field system?
4. charge moves a distance of 2.0 cm in the direction of a uniform electric field whose magnitude is 215 N/C. As the charge moves, its electrical potential energy decreases by 6.9 x10-19 J. Find the charge on the moving particle. What is the potential difference between the two locations?
1. Two point charges q1 = +26µC and q2 = −17.5µC are 64 cm apart.a. What is the potential energy of the system of two charges?b. What is the electric potential at a point between them 24 cm from q1?
34. I need help with these questions. The question reads: A uniform electric field has magnitude 240 N/C and is directed to the right. A particle with charge +4.2 nC moves along the straight line from a to b. a) what is the electric force that acts on the particle? B) what is the work done on the particle by the electric field? C) what is the potential difference Va-Vb between points a and b?
5. Three point-like charges are placed at the corners of a rectangle as shown in the figure, a = 38.0 cm and b = 48.0 cm. q2 = +3.30 μC, Find the work done by the electric field force when the charge q2 is moved to infinity. Let q₁ = -2.50 µC, 93 = +3.60 μC. J f60 ssf60 s too s ai 91 ssf60 ssf60 ssf60 ssf60 ssf60 ssfóð 09js (9) 09.19js (9js (9jss 93 ssf60 ssss$60 ssf60 sst ssf6092 oss is mos f60 ssf60 ssf60 ssf60 ssf60 ssf60 50 ssf60 ssf60 ssf
10. You need a coaxial cable that can hold ± 62 nC/m of charge density. Someone hands you a cable with a 2.0 mm diameter inner conductor and 1.6 cm outer conductor (see diagram at right). The maximum potential difference the cable will tolerate is 2 kV. Will this cable work for your application? a-
Consider a charge of -2.0 mC between two charged parallel plates as shown below. What will be the change in the potential energy (AU) of this charge when it is moved from point B to point A if the potential difference AV (=Vg-Vg) is +1000 V? А. -2.0J B. +2.0 J C. -2000 J А В D. +2000 J Е. ОJ + + + + +