IIT JEE , AIEEE Forum - Physics , Electricity

magiclko

Any of the Experts, plsss reply...i'll be gr8ful

For a Shell with inner radius "r" n outer radius R having a charge Q(+ve) at the centre, what is the expression for its Self-Energy and also for Potential Energy??? is this system will be formed on its own???? and if in place of +Q, what would hav been the result, if -Q would hav been thr at the centre???

plsss reply....m quite confused bout this concept

!!!

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Tuff Tym never Lasts, tuff people do.....

magiclko

no reply

krishna.gopal

HI magician, Sorry for the delayed reply. Well before answering your question i would like to tell you something about the concept of self energy. Then i would like that you answer your question yourself as that will be a nice approach.

Lets start with the concept of potential energy.

1) Suppose there are two point charges(q1 and q2) seperated by distance r. When we say that it is Kq1q2/r then it is the work done to bring q1 and q2 from infinite seperation to distance r.(Where K is proportionality constant)

2) Now suppose we want to find the potential energy of a charge Q₁ placed at the centre of a shell of radius r, which contains a charge Q₂.

Suppose to begin with there is only charge Q₁ at the center of a neutral shell. Now we start bringing infinetisimal charges dq to the shell. Let at any time shell contain charge q.Increase in potential energy by adding another charge dq to the shell is given by

dU = KQ₁dq/r+Kqdq/r

Therefore potential energy of the system

U =₀

^Q2dU=K(Q₁Q₂/r)+(1/2)K(Q₂²/r)

The first term of this energy is called interaction emergy as this is enegy associated with interaction of point charge with charge on shell while the second term is called self energy as it is the energy of interaction between charges on the shell itself.

I think that this example clears you difference self enrgy and interaction energy. The sum of both the energies is called total potential energy..

I hope this example will make you understand the concept of self energy. Now try to calculate self energy for your problem and in case you can't solve it let me know.

magiclko

Thanx Aloot, for the concept

...

the self energy that i hav calculated is

K (Q²/2) {(1/r)-(1/R)}

but in some bokks its written that this is the total potential enrgy.... is it so???

n also pls give the full solution to that problem

krishna.gopal

Well magiclko (waise what is ur real name if u don't mind) there is some mistake in ur calculation.

First since self enegry comes becaose of interaction between similar charges so it can never be negative (u can't have -KQ²/R)

Lets for calculation of potential energy we define Q charge at centre as 1 -Q on inner shell as 2 and +Q on outer shell as 3

The total potential energy has five terms

Self energy of 2=KQ²/(2r)

Self energy of 3=KQ²/(2R)

Interaction of 1&2=-KQ²/r

Interaction of 1&3=KQ²/R

Interaction of 2&3=-KQ²/R

So total self energy =KQ²/2(1/r+1/R)

Total interaction enrgy =-KQ²/r

Total potential energy=(-KQ²/2)(1/r-1/R)

magiclko

thanx.... i think i was mistaking for the concept.....

nd yes....my name is "manasi"....waise, its thr in the signature.... u wont hav noticed!!! thanx once again!!

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