Inductance and Charge Redistribution

[Ayesha02]

@Ayesha02 if you haven't solved differential equations before, then suppose that $f (t)=A\cos (\omega t-B)$ and use the initial conditions I hinted at in a previous post to find the unknowns.

ohh thanks buddy!

 

[Delta2]

@Ayesha02 can you please tell me from which book is this exercise , for me at least it represents a fine blending of electrostatics with circuit theory ,and I just want to know from which book it is.

 

[etotheipi]

@Ayesha02 can you please tell me from which book is this exercise , for me at least it represents a fine blending of electrostatics with circuit theory ,and I just want to know from which book it is.

I agree, it's quite a fun question. Am interested also!

 

[Ayesha02]

Are you guys from India, by any chance?
We have a real tough exam here that we've to appear, and this is one of the questions from our preparatory material.

 

[archaic]

@Ayesha02 can you please tell me from which book is this exercise , for me at least it represents a fine blending of electrostatics with circuit theory ,and I just want to know from which book it is.

Probably from Irodov's problems in general physics or a JEE problems textbook.

 

[rude man]

So
My textbook's solution says that :

angular frequency of the LC oscillation is w=sqrt( 2*pi*$E_0$*R*L)
And that required time is one fourth of time period

Can you explain this please @rude man @archaic

You have written $\epsilon_0$ a wrong way.
I further think you copied wrong because that answer is dimensionally incorrect.
How about you left out a "1/"?
That answer would be correct.

 

[Ayesha02]

You have written $\epsilon_0$ a wrong way.
I further think you copied wrong because that answer is dimensionally incorrect.
How about you left out a "1/"?
That answer would be correct.

yeah i got that...i missed the reciprocal

although, could you help me understand the solution theyve given?

 

[rude man]

yeah i got that...i missed the reciprocal

although, could you help me understand the solution theyve given?

The charge oscillates back and forth between the two spheres at that radian frequency.
The only way you're going to get the answer is by solving the differential equation. There are a number of ways to do that, for example the way a previous poster suggesting a solution of the form $cos(\omega t - \phi)$, $\phi$ a constant.

 

[Ayesha02]

The charge oscillates back and forth between the two spheres at that radian frequency.
The only way you're going to get the answer is by solving the differential equation. There are a number of ways to do that, for example the way a previous poster suggesting a solution of the form $cos(\omega t - \phi)$, $\phi$ a constant.

Ohh finally!
understood:)

 

[archaic]

although, could you help me understand the solution theyve given?

What have you got up until now from solving the differential equation?

 

[rude man]

Additional comment: it is an interesting probem because it makes concrete the nexus between 'potential' of physics and 'voltage' of electrical engineering.

 

[etotheipi]

Additional comment: it is an interesting probem because it makes concrete the nexus between 'potential' of physics and 'voltage' of electrical engineering.

Yeah, there are a few different ways you could think about it. Either a closed loop to infinity and back, in which case you can treat the potential as the potential difference between the sphere and infinity: $\frac{kQ_A}{r} - L\frac{di}{dt} - \frac{kQ_B}{r}$. Or you could think about it in the sense of two potentials $\frac{kQ_A}{r}$ and $\frac{kQ_B}{r}$ and a potential difference between them...

Can blur the lines a little but but usually the distinction is that to discuss potential we have a fixed reference, so it means being extra careful when discussing the potential relative to another arbitrary point (really differences) as opposed to a potential relative to the fixed reference.

 

[Ayesha02]

Guys I have a lot of these kinda problems just follow me and stay tuned so that we have more of these discussions.

The most recent one i have put up goes by the title- 'Hard Momentum Conservation'
See u there:)

 

[etotheipi]

See u there:)

Sorry, I had to:

 

[Ayesha02]

Guys I have a lot of these kinda problems just follow me and stay tuned so that we have more of these discussions.

The most recent one i have put up goes by the title- 'Hard Momentum Conservation'
See u there:)

@etotheipi I need u there my man:)

 

[rude man]

Sorry, I had to:

We badly need some humor on this site. We all love physics but we need to take even it a bit more lightly now and then. Thank you! (Of course this song always reminds me of 'Dr. Strangelove' too.)

 

[rude man]

Guys I have a lot of these kinda problems just follow me and stay tuned so that we have more of these discussions.

The most recent one i have put up goes by the title- 'Hard Momentum Conservation'
See u there:)

We helpers love to help! Really! Forces us to review also, often; so in a sense you're a helper too! And all of us love physics all the time!

 

[etotheipi]

We badly need some humor on this site. We all love physics but we need to take even it a bit more lightly now and then. Thank you! (Of course this song always reminds me of 'Dr. Strangelove' too.)

Especially now that cabin fever has fully set in