1. Questions

Physics-Gauss' Law, hard

Thank you Damon for answering my first questions fast and accurately. Do you or anybody else know how to do these harder Gauss' Law Problems?

1. A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q.
a) Describe the electric field lines both inside and outside the spheres (as if you had to draw field lines on the chart-no calculations).
b) Use Gauss' law to find an expression for the magnitude of the electric field between the spheres at a distance r from the center of the inner sphere (R<r<3R)
c) Calculate the potential difference between the two spheres.
d) The spheres are then connected by a conducting wire for long enough that the charges can redistribute. What is the final distribution charge on the two spheres?
e) The wire connecting the spheres is removed and the outside sphere is grounded. What is the charge distribution on the two spheres?

2. A long, insulating cylinder has a uniform charge density, ro=-2*mu*C/m^3, and a radius, R=15cm.
a) What is the total charge on a 40cm length of that cylinder?
b) Use Gauss' Law to find the electric field both inside and outside of the cylinder as a function of the distance from the center of the cylinder, r.
c) Set up an integral to evaluate the potential at the surface of the cylinder (dont solve).
An isolated (ungrounded) conducting shell of inside radius 30cm and outside radius 40cm is now snapped together around the insulating cylinder.
d) What is the effect (qualitative) on the electric field at r=50cm?
e) What is the effect (qualitative) on the potential at the surface of the insulator.

  1. 👍 0
  2. 👎 0
  3. 👁 685
Bobby

  1. a)
    inside the inner sphere, a closed spherical surface encloses no charge, so E is 0
    between spheres, the outer sphere is irrelevant, only the 2 Q matters
    E drops off with 1/r^2, the surface area of spherical surface.
    outside sphere 2
    we surround a total of 2Q-Q = 1 Q
    field again drops off as 1/r^2

    b)
    R<r<3R
    E = 2 Q/(4 pi r^2 eo)

    c)
    integral E dr = [Q/(2 pi eo)] dr/r^2
    = [Q/(2 pi eo)] [-1/r] at 3R - at 1R
    = [Q/(2 pi eo)] [ -1/3R +1/R ]
    = (2/3)[Q/(2 pi eo R)]
    = Q/(3 pi eo R)

    d) the E between spheres must be zero or there would be a potential difference between spheres, so all charges must move to the outer sphere, net 1 Q

    e) all gone.

    1. 👍 0
    2. 👎 0
    Damon

  2. Damon, you are amazing...
    Tell me if you get the second one please, I'm still having trouble.
    In the meantime I temporarily took over your role answering all the math questions =].

    1. 👍 0
    2. 👎 0
    Bobby

  4. 2. A long, insulating cylinder has a uniform charge density, ro=-2*mu*C/m^3, and a radius, R=15cm.
    a) What is the total charge on a 40cm length of that cylinder?
    volume of .4 m length = pi r^2 L = pi (.15)^2 (.4) = .02827 m^3
    Q = ro * volume = -.05655 *10^-6
    = -5.66*10^-8 C
    b) Use Gauss' Law to find the electric field both inside and outside of the cylinder as a function of the distance from the center of the cylinder, r.
    E
    inside
    Q enclosed = ro pi r^2 L
    area of Gauss surface = 2 pi r L
    E = Qenclosed/area eo = ro pi r^2 L/2 pi r L eo
    = ro r/2 eo
    outside
    E = Q at R length L / 2 pi r eo L
    = ro pi R^2 L / 2 pi r eo L
    = ro (R^2/r)/2 eo
    E *area = Qenclosed / 4 pi r^2 eo

    c) Set up an integral to evaluate the potential at the surface of the cylinder (dont solve).

    well, I suppose we call it 0 at the center so
    integral E dr = integral inside
    = (ro /2 eo) r dr

    An isolated (ungrounded) conducting shell of inside radius 30cm and outside radius 40cm is now snapped together around the insulating cylinder.
    d) What is the effect (qualitative) on the electric field at r=50cm?

    still surround the same old charge, -Q moves inside, + Q moves to outer surface. No effect

    e) What is the effect (qualitative) on the potential at the surface of the insulator. No effect

    Now if you ground that conducting shell, that kind of defines your zero of potential there, whereas I defined it at the center of the problem. That would change Voltages but not voltage differences.

    1. 👍 0
    2. 👎 0
    Damon

  5. Thank you so much Damon!

    1. 👍 0
    2. 👎 0
    Anonymous

  6. e,

    1. 👍 0
    2. 👎 0
    Musa

Respond to this Question

First Name

Your Response

Similar Questions

  1. Test taking Stratagies (2 questions) help me plz

    1.)Which of the following is a good way to approach answering an essay question on a test? A.)Start writing your answer as soon as you have read the question B.)Jot down a rough outline before you start writing**** C.)Write as

  2. math

    If 90% of the households in a certain region have an answering machines and 50% have both answering machines and call waiting, what is the probability that a household chosen at random and found to have an answering machine also

  3. math

    alan scored a total of 14 points for answering all 15 questions on a math quiz for every correctly answered question alan got 2 points for every wrong ahe lost 2 points how many questions did he answer correclty

  4. probability

    What is the probability of getting 80% or more of the questions correct on a 10-question true-false exam merely by guessing? probability - Damon, Wednesday, March 6, 2013 at 2:53am Binomial distribution with p = .5 p(10 right) =

  1. HElp MaTh PleasE!

    A multiple choice test has 5 questions each with 5 possible answers. Find the probability of answering all the questions correctly. A. 1/3,125 B. 1/25 C. 1/625 D. 1/125 How do you do this problem?

  2. Math

    Kosuke wrote a mathematics contest consistingof 25 multiple choice questions, the scoring system gave 6 points for a correct answer, 2 points for not answering, and 1 point for an incorrect answer.Kosuke got x correct and left y

  3. science

    Define inductive reasoning. answering questions by analyzing specific observations and using them to come to a more general understanding doubting or not accepting conclusions or ideas until they have been adequately tested and

  4. English

    In English, we're learning about the Holocaust and we are answering to "related-to-your-life" questions and below are some questions that I do not understand. Please help! Thank you. Does the U.S. control any countries? Do we have

  1. MATH!

    A multiple choice test has 5 questions each with 5 possible answers. Find the probability of answering all the questions correctly. A. 1/3,125 B. 1/25 C. 1/625 D. 1/125 Is it B?

  2. MATH

    On a TV game show, a contestant makes $600 for every correct answer but loses $500 for every wrong answer. After answering 22 questions, Sarah broke even. How many questions did she answer correctly?

  3. Finance

    Damon Enterprises' stock is currently selling for $25.00 per share. The stock's dividend is projected to increase at a constant rate of 7% per year. The required rate of return on the stock, rs, is 10%. What is Damon's expected

  4. math

    alan scored a total of 14 points for answering all 15 questions on a math quiz for every correctly answered question alan got 2 points for every wrong ahe lost 2 points how many questions did he answer correclty

You can view more similar questions or ask a new question.