anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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goformit100
  • goformit100
Wher is it ?
anonymous
  • anonymous
|dw:1361637181191:dw| Given \[q_1=-q_2\] I have to find the potential difference. Here is what I got so far..... \[V_1=\frac{kq_1}{r_1}\rightarrow q_1=\frac{V_1r_1}{k}\] \[V_2=\frac{kq_2}{r_2} \rightarrow q_2=\frac{V_2 r_2}{k}\] \[V_1 r_1=-V_2r_2\] \[V_1r_1+V_2r_2=0\] but I have to get delta V
anonymous
  • anonymous
I probably shouldn't cancel out the k's

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anonymous
  • anonymous
the k's do cancel out. I tried it another way \[\frac1k(V_1r_1-V_2r_2)=0\]
TuringTest
  • TuringTest
q1 is in the inside?
anonymous
  • anonymous
q_1 is on the inside and it's positive q_2 is on the outside and it's negative
anonymous
  • anonymous
I can set q_1 equal to q_2 correct? since they are equal but opposite in charge?
TuringTest
  • TuringTest
yes, so you can factor it out by superposition\[\sum_i\vec E_i=\frac q{4\pi\epsilon_0r_i}\]
anonymous
  • anonymous
elaborate.... how did we add the electric field into the equation?
TuringTest
  • TuringTest
I'm trying to do this from scratch, but I guess I'm a little rusty, hold on please
anonymous
  • anonymous
yeah no prob :)
TuringTest
  • TuringTest
\[\Delta V=-\int\limits_C\vec E\cdot d\vec\ell=-\frac q{4\pi\epsilon_0}\int_a^b\frac{dr}{r^2}\]or is it 2q... I should find something to double-check, but the rest is right
anonymous
  • anonymous
anonymous
  • anonymous
oh I see....
TuringTest
  • TuringTest
it's just q, but you are using a different formula
TuringTest
  • TuringTest
your formula is the same, of course. You are probably just highlighting the connection to potential energy and voltage.
anonymous
  • anonymous
Does that mean that \(q=k\Delta Vr\) ?
TuringTest
  • TuringTest
\[q=k\Delta Vr=\frac1{4\pi\epsilon_0}\cdot\frac q{4\pi\epsilon_0 r^2}\cdot r\]so no :p
anonymous
  • anonymous
how about this: \[\Delta V=-\frac Er\] \[\frac{kq}{r}=-\frac E r\] \[q=\frac{-E} k\]
anonymous
  • anonymous
LOL I don't know ...haha
TuringTest
  • TuringTest
for the other, I eant\[q\neq\Delta Vr=\frac1{4\pi\epsilon_0}\cdot\frac q{4\pi\epsilon_0 r}\cdot r=\frac q{(4\pi\epsilon_0)^2}\]about your next one\[\Delta V=-\frac{Er}q\]\(if\) E and r are in the same direction whe whole time
anonymous
  • anonymous
I think they are int he same direction since |dw:1361640455529:dw| correct?
TuringTest
  • TuringTest
in this case, yes
anonymous
  • anonymous
oh yay! So what would we do with that relationship? \[\Delta V=-\frac{Er}q\]
TuringTest
  • TuringTest
yes, as long as the path we are checking voltages between is parallel to the electric field lines
anonymous
  • anonymous
do we assume that that is the path?
anonymous
  • anonymous
It probably wouldn't be parallel
TuringTest
  • TuringTest
yeah, I mean the displacement really, we could go in the path|dw:1361640896393:dw|but the *displacement* is all that matters for calculating voltage if the field lines are parallel to it
anonymous
  • anonymous
Oh I see...
TuringTest
  • TuringTest
|dw:1361641026090:dw|
TuringTest
  • TuringTest
we need the more general line integral for for things where the E-field is not parallel to the displacement at all times, like|dw:1361641180439:dw|where a charge is going like...
TuringTest
  • TuringTest
|dw:1361641482262:dw|better prediction of the path of the charge in such a field^
anonymous
  • anonymous
since we have a sphere, it shouldn't have a potential difference on it's own. But it has a constant potential.....so: no potential difference on a sphere? just between spheres?
TuringTest
  • TuringTest
if there were a potential difference between one part of a conducting sphere and another, current would flow across it until the potential difference was neutralized
TuringTest
  • TuringTest
what's the question?
anonymous
  • anonymous
\[\frac{kq}{r}=E\cdot r\] \[q=\frac{E\cdot r}{k}\] I'm soo stuck....LOL! But it seems sooo simple!
TuringTest
  • TuringTest
in that case, all it's basically asking is for you to find\[\Delta V=\frac1q\Delta U=k(E_{outside}-E_{insode})\]and since |Q1|=|Q2| in this case, we can factor it out to give\[\Delta V=-kE\Delta r=-\frac Q{4\pi\epsilon_0}\left(\frac1{r_2^2}-\frac1{r_1^2}\right)\]
anonymous
  • anonymous
How did you get the \(-kE\Delta r\) part?
TuringTest
  • TuringTest
so many typos, my connection is terrible getting a new computer soon last line should be\[\Delta V=-\frac1QE\Delta r\] but really this is better seen as an integral..\[\Delta V=-\int_a^b Edr=1\frac Q{4\pi\epsilon_0}\int_a^b\frac{dr}{r^2}\]I don't know what else to say right now... go wat and think of a more definitive question to ask!
anonymous
  • anonymous
I'll go eat....I wanna walk away from this problem for a little bit....
anonymous
  • anonymous
It will probably make more sense then LOL.
TuringTest
  • TuringTest
yes, it is quite simple and you are over-thining it see you later, I am learning a little statistics
anonymous
  • anonymous
see ya Turing!

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