IIT JEE , AIEEE Forum - Physics , Electricity - 2 METAL SPERES OF RADII R1 N R2 R KEPT WIDE APART, WHAT WILL BE THEIR CAPACITANCES????

Terminator.HCV

2 METAL SPERES OF RADII R1 N R2 R KEPT WIDE APART, WHAT WILL BE THEIR CAPACITANCES????

feynmann

beyond the syllabus !!

Exact approach using conformal mapping gives result involving inverse hyperbolic functions !!

but since the distance between them is large, approximate solution can be found which is well within the syllabus !!

anchitsaini

Feynmann , can't we do it by finding the total energy of the system ie interaction energy + self energy and put it = Q^2 / 2C

to get C ie capacitance ?

feynmann

Yes !

but the problem lies on calculation of interaction energy !!

Terminator.HCV

by the way, Richard, i think a probable soln. would be by considering each of the sphere as inside another(concentric) n considering the outer one to be at infinite seperation.

C=(4.pi.e0.a*b)/(a+b)
or, C=(4.pi.e0.a)/(a/b+1) i.e. dividing num & den by b
Now, Limit(B tends to 0) C gives : C=4.pi.e0.a

Wouldn't this do?????
Correct me if I am wrong......

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a_JOSHI

i think its in d syllabus..
see c=q/v
v=q/4 pi eplsionnaught (1/r1-1/r2)
so c=4 pi epsilonnaught (r2-r1)/r1r2
please rate if i m correct...
i think this is correct

mukulaish

Why is nt the answer R1/k and R2/k??

When they r kept wide apart, why shud they be interacting wid each ohter??

Pls explain......

Terminator.HCV

By the way Richard, this problem is from HC VERMA, Capacitors, Problem no. 12. I hope Verma is not out of syllabus..........

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riku

Vaah terminator,, tune toh forum expert ko bhi nahi baksha!! nice..

Yups ,, now answering seriously,, the question stated by u,, itself states dat the spheres are kept at a wide distance,, their interaction will be minimum , so while calculating their individual capacitances, the interaction of the other wont be considered ,, or as earlier quoted dat ,, it can be considered dat the other capacitor lies at infinite distance,, their individual capacitances become $4\pi {\epsilon}_{0} {R}_{1}$ and $4\pi {\epsilon}_{0} {R}_{2}$ ..

What was hard in this?/ But the question would have been tricky if u would have asked,, that what will be capacitance of the system ,, if they are joined by any conductor(or medium made conducting),, then after calculating individual capacitances ,, the connection would be like two parallel capacitors ,,, so simply add them..

I would add that,, yes if distance would have been finite,,, then one has to consider induction and calculation of interaction energy would have been done by conformal mapping....

maza aaya... rate me quick..

Terminator.HCV

Theres only one mistake in my "Most Probable" ans. I stated the concentric spheres 2 b at infinte sepratn; please read it as infinite radius and the problem is done. Thankx to everybody for helping.

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feynmann

Hey Guys , just try to understand !!

What do u mean by the phrase "seperated by a long distance " ?

If that means that the distance between them is infinity then there is no qn of interaction , we have simply two non-interacting metal spheres whose total capacitances are simply the sum of their individual capacitances .

But if they are seperated by finite distance ( say d ) then I must admit that the situation is really bad !!

If anybody can calculate for finite seperation using class XII approach , I myself would give him 10 hats !!

Promise !!

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