kihr
Feb20-10, 09:58 AM
1. The problem statement, all variables and given/known data
A spherical shell of radius 'a' and charge Q is expanded to radius 'b'. What is the work done by the electrostatic force in this process?
2. Relevant equations
Method 1
Work done = initial energy - final energy
Method 2
Work done = Q (potential difference between the two positions)
3. The attempt at a solution
Method 1
Initial energy of the spherical capacitor = Q*Q / 2C
= Q*Q / 2*4*pi*E*a (E= permittivity of the medium)
Final energy = Q*Q / 2*4*pi*b
Work done = Q*Q / 2*4*pi*E [ 1/a - 1/b]
Method 2
Initial potential = Q / 4*pi*E*a
Final potential = Q / 4*pi*E*b
Work done = Q*Q / 4 *pi* E* [1/a - 1/b]
The two methods do not lead to the same answer. I need to understand why this is so. Would appreciate some tips. Thanks.
A spherical shell of radius 'a' and charge Q is expanded to radius 'b'. What is the work done by the electrostatic force in this process?
2. Relevant equations
Method 1
Work done = initial energy - final energy
Method 2
Work done = Q (potential difference between the two positions)
3. The attempt at a solution
Method 1
Initial energy of the spherical capacitor = Q*Q / 2C
= Q*Q / 2*4*pi*E*a (E= permittivity of the medium)
Final energy = Q*Q / 2*4*pi*b
Work done = Q*Q / 2*4*pi*E [ 1/a - 1/b]
Method 2
Initial potential = Q / 4*pi*E*a
Final potential = Q / 4*pi*E*b
Work done = Q*Q / 4 *pi* E* [1/a - 1/b]
The two methods do not lead to the same answer. I need to understand why this is so. Would appreciate some tips. Thanks.