- #1
vboyn12
- 16
- 2
- Homework Statement
- In photo below. (help me please)
- Relevant Equations
- I don't know whether the relevant equation can help because I haven't figure out any idea yet.
Hi, I try to solve part a and b and i posted below, can you have a look at it?BvU said:Hi,
PF rules (please read them) only allow us to help if you post an attempt at solution.
What have you learned so far, that you might use here?
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BvU said:OK, so you use $$ V_1-V_2 = 12\ \text{V}\ = {Q\over 4\pi\varepsilon_0}\left ( {1\over r_1} - {1\over r_2} \right ) $$(which I suppose might make a good entry in the list of relevant equations )
And then (another one !) $$ \left | \vec E(r_s) \right | = {Q\over 4\pi\varepsilon_0}\ {1\over r_s^2} $$so that $$ \left | \vec E(r_s) \right | = { 12\ \text{V}\ \over \ \displaystyle {1\over r_1} - {1\over r_2}\ } \ {1\over r_s^2} =
12\ \text{V}\ {1\over r_2-r_1}\;{r_1 r_2\over r_s^2 }$$(thus avoiding calculator and rounding errors!) which agrees with your result once we learn to read your handwritten 4 that looks scaringly similar to a 9
I wouldn't quote 6 digits if the ##r## are given in only 1 digit, but that's a matter of taste.
Be sure to use the right ##\varepsilon## if you quote so many digits (I get ##|D| = 1.312 \ 10^{-9} ## !) and do use units !
For part c) you need to know that at least the inner sphere is non-conducting !
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Sorry about the unit :D. For part (c), is that the value of charge Q found in part (a) equal to the surface charge density multiply by the surface area which is 4pi*r^2? If that is right I get rho(s)=11,789 nC/m^2BvU said:OK, so you use $$ V_1-V_2 = 12\ \text{V}\ = {Q\over 4\pi\varepsilon_0}\left ( {1\over r_1} - {1\over r_2} \right ) $$(which I suppose might make a good entry in the list of relevant equations )
And then (another one !) $$ \left | \vec E(r_s) \right | = {Q\over 4\pi\varepsilon_0}\ {1\over r_s^2} $$so that $$ \left | \vec E(r_s) \right | = { 12\ \text{V}\ \over \ \displaystyle {1\over r_1} - {1\over r_2}\ } \ {1\over r_s^2} =
12\ \text{V}\ {1\over r_2-r_1}\;{r_1 r_2\over r_s^2 }$$(thus avoiding calculator and rounding errors!) which agrees with your result once we learn to read your handwritten 4 that looks scaringly similar to a 9
I wouldn't quote 6 digits if the ##r## are given in only 1 digit, but that's a matter of taste.
Be sure to use the right ##\varepsilon## if you quote so many digits (I get ##|D| = 1.312 \ 10^{-9} ## !) and do use units !
For part c) you need to know that at least the inner sphere is non-conducting !
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No problem for me, but it can save you brownie points with graders...vboyn12 said:Sorry about the unit :D
Do you get the same result as mine for part (c)?BvU said:Up to you: the usual symbol for surface charge is ##\sigma\;##, and ##\rho\ ## is usually volume charge density. Hence my speculation in post #5.
No problem for me, but it can save you brownie points with graders...
It is not conductingBvU said:What does it say in the actual problem statement ? Is it a conducting sphere or not ?
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can you give me your solution corresponding to your assumption, please?BvU said:And is the charge uniformly distributed over the volume ?
(That is my assumption -- and in that case I don't agree with your answer)
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Oh, I see :D. Thank you a lotBvU said:You mean calculate the charge density in a uniformly charged unconducting sphere with a given total charge ##Q\ ## ?##\ ##
Electric field intensity/density is a measure of the strength of an electric field at a given point. It is a vector quantity that describes the direction and magnitude of the force that a charge would experience if placed at that point.
The electric field intensity/density is directly proportional to the potential difference between two points. This means that a larger potential difference will result in a stronger electric field, and vice versa.
The formula for electric field intensity/density is E = V/d, where E is the electric field intensity/density, V is the potential difference, and d is the distance between the two points.
The SI unit for electric field intensity/density is volts per meter (V/m). However, it can also be expressed in other units such as newtons per coulomb (N/C) or volts per centimeter (V/cm).
To find electric field intensity/density with a given potential difference, simply plug in the values for V and d into the formula E = V/d. Make sure to use consistent units for V and d. The resulting value will be the electric field intensity/density at the given point.