Solved

Capacitance of the Earth

Posted on 2007-04-05
6
4,696 Views
Last Modified: 2008-02-01
a) Discuss how the concept of capacitance can also be applied to a _single_ conductor (hint: In the relationship C = Q/V, think of the second conductor as being located at infinity).

I'm not really sure how to approach this. If I say that each conductor is infitely far apart then I can regard them both as point charges. In which case:

 V = lim r->inf [ k * q_1 * q_2 / r ] = 0

So I'm not understanding how to apply this hint.


b) Use C=Q/V to show that C = 4pi(epsilon_0) * R for a solid conducting spehre of radius R.

I think I need to get part (a) first.

c) Use your result in part (b) to calculate the capacitance of the earth, which is a good conductor of radius 6380km, compare to typical capacitors used in electronic circuits that have Capacitances from 10 pico farad to 100 micro farad




I just need help getting started.
0
Comment
Question by:BrianGEFF719
6 Comments
 
LVL 84

Accepted Solution

by:
ozo earned 150 total points
ID: 18862599
What's the voltage of a charge Q on a sphere of radus r?
0
 
LVL 27

Assisted Solution

by:d-glitch
d-glitch earned 100 total points
ID: 18863368
You can't start with point charges.
You have to start with a sphere.

Put a charge Q on a spere of radius r, calculate the E field (magnitude and direction), and think about where it goes to zero.

The dimensions of an E field are volts/meter, so if you integrate along a field line you will get a voltage.


0
 
LVL 25

Assisted Solution

by:InteractiveMind
InteractiveMind earned 150 total points
ID: 18863379
b)

Gauss's Law for E:  Integral{over S} E•dS = Sum_of Q/eps_0

thus:

E(4*PI*r²) = Q/eps_0

E = Q / (4*PI*r²*eps_0)

E = V/r, hence:

V = Q / (4*PI*r*eps_0)

C = Q/V = 4*PI*r*eps_0
0
Live: Real-Time Solutions, Start Here

Receive instant 1:1 support from technology experts, using our real-time conversation and whiteboard interface. Your first 5 minutes are always free.

 
LVL 25

Assisted Solution

by:InteractiveMind
InteractiveMind earned 150 total points
ID: 18863519
Better yet:

Coulomb's Law:  E = Q / (4*PI*r²*eps_0)

V= - Integral E dr, per se d-glitch's comment;

V = - Integral Q / (4*pi*r²*eps_0) dr

And so on
0
 
LVL 25

Expert Comment

by:InteractiveMind
ID: 18864164
By the way, it would seem that the permittivity of a conductor affects it's capacitance; so I think it should really be:
C=4*PI*r*eps_s
(where eps_s, the static permittivity, =eps_0*eps_r)
0
 
LVL 27

Assisted Solution

by:aburr
aburr earned 100 total points
ID: 18864680
When your problem suggested that you consider the other conductor to be at infinity, it was not suggesting that it be a point at infinity, but was suggesting that the other conductor be a sphere with an infinite radius. The potential of that very large sphere can be taken to be zero.
The permitivity to be used is the permitivity of the medium in which the electric field lines exist. In this case, free space. (There are no field lines inside a conductor.)
Modern capacitors can have values greater that 1 farad.
0

Featured Post

Gigs: Get Your Project Delivered by an Expert

Select from freelancers specializing in everything from database administration to programming, who have proven themselves as experts in their field. Hire the best, collaborate easily, pay securely and get projects done right.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Solving an equation 8 63
Discrete Values 2 50
Binomial distribution 2 55
PHP Loan Calculation formula help. 8 79
Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

785 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question