Q75P Two metal spheres of different s... [FREE SOLUTION]

91影视

University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 4: Q75P (page 782)

Two metal spheres of different sizes are charged such that the electric potential is the same at the surface of each. Sphere A has a radius three times that of sphere B. Let Q_A and Q_B be the charges on the two spheres, and let E_A and E_B be the electric 颅field magnitudes at the surfaces of the two spheres. What are (a) the ratio Q_B/Q_Aand (b) the ratio E_B/E_A?

Short Answer

Expert verified

(a) The ratio Q_B/Q_A is 1/3.

(b) The ratio E_B/E_A is 3.

Step by step solution

Step 1:

We are given two metal spheres A and B with the same electric potential VA = VB. Also, we are given the radius of the two spheres where R_A=3R_B

The relation between the charges of the two sphere and electric potential due to the charged sphere is $V = \frac{1}{{蟿蟿蔚}_{o}} \frac{q}{R}$

Where $\frac{1}{4 蟺 {\overset{藱}{o}}_{掳}} = 9.0 脳 10^{9} N . m^{2} / C^{2}$ , R is the radius of the sphere and q is the charge on the sphere.

For the spheres obtain:

role="math" localid="1664266286684" $V_{A} = V_{B} \frac{1}{4 蟺 {\overset{藱}{o}}_{掳}} \frac{Q_{A}}{R_{A}} = \frac{1}{4 蟺 {\overset{藱}{o}}_{掳}} \frac{Q_{B}}{R_{B}} \frac{Q_{A}}{3 R_{A}} = \frac{Q_{B}}{R_{B}} (\frac{Q_{B}}{R_{B}}) = \frac{1}{3}$

Therefore, the ratio Q_B/Q_A is 1/3.

Step 2:

The electric field at the surface of a charged sphere is $E = \frac{1}{4 {蟿蟿蔚}_{掳}} \frac{| Q |}{R^{2}}$

Get the desired ration by dividing E_Bby E_A

$(E_{B} / E_{A}) = \frac{(Q_{B} / R_{B}^{2})}{(Q_{A} / R_{A}^{2})} (E_{B} / E_{A}) = \frac{Q_{B}}{Q_{A}} {(\frac{R_{A}}{R_{B}})}^{2} (E_{B} / E_{A}) = \frac{Q_{B}}{Q_{A}} {(\frac{3 R_{A}}{R_{B}})}^{2} (E_{B} / E_{A}) = \frac{1}{3} {(3)}^{2} (E_{B} / E_{A}) = 3$

Therefore, the ratio E_B/E_A is 3.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Step 1:

Step 2:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Physics of Motion

Astrophysics

Electricity and Magnetism

Electric Charge Field and Potential

Particle Model of Matter

Study anywhere. Anytime. Across all devices.