Goddar
Sep3-08, 09:35 PM
1. The problem statement, all variables and given/known data
Infinite parallel-plates capacitor (distance = d), opposite charge densities (+/– sigma); NO OTHER INFORMATION GIVEN... questions:
a) determine 9 elements of stress tensor
b) determine force per unit area on top plate (+ sigma)
c) What is the momentum per unit area and time crossing a plane between the plates?
d) At the plates, this momentum is absorbed and plates recoil; find it and compare to (b)
2. Relevant equations
Too many of them; i'll give my thoughts in words..
3. The attempt at a solution
I insist that no other prior information is given, so as far as we know there is no net current flowing anywhere.. In that case, how could there ever be a B-field?
if there is no B-field, by the definitions of the book, there is no Poyinting vector, and thus no EM-momentum; but we have a force, so there really should be one..
This is where i'm lost...
a) all i can get is the Tzz component, which is (sigma)2/2epsilon0;
b) integrating the above along the z-axis, i get the same expression multiplied by d (distance between plates)
(c) and (d) are irrelevant, considering that... What's my problem, here?..........
Infinite parallel-plates capacitor (distance = d), opposite charge densities (+/– sigma); NO OTHER INFORMATION GIVEN... questions:
a) determine 9 elements of stress tensor
b) determine force per unit area on top plate (+ sigma)
c) What is the momentum per unit area and time crossing a plane between the plates?
d) At the plates, this momentum is absorbed and plates recoil; find it and compare to (b)
2. Relevant equations
Too many of them; i'll give my thoughts in words..
3. The attempt at a solution
I insist that no other prior information is given, so as far as we know there is no net current flowing anywhere.. In that case, how could there ever be a B-field?
if there is no B-field, by the definitions of the book, there is no Poyinting vector, and thus no EM-momentum; but we have a force, so there really should be one..
This is where i'm lost...
a) all i can get is the Tzz component, which is (sigma)2/2epsilon0;
b) integrating the above along the z-axis, i get the same expression multiplied by d (distance between plates)
(c) and (d) are irrelevant, considering that... What's my problem, here?..........