Consider a infinitely large parallel plate capacitor, with the lower plate (at z = -d/2) carrying...

 

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Consider a infinitely large parallel plate capacitor, with the lower plate (at z = -d/2) carrying the charge density -, and the upper plate (at z = +d/2) carrying the charge density +. + a) [15 pts] Calculate all nine elements of the Maxwell stress tensor T in the region between the plates, and write out the results in a 3 3 matrix. Also determine the Poynting vector S in the region between the plates. b) [10 pts] Find the force per unit area on the top plate using your T, using the relation: d F = T dA COMO S dr. In this formula, F is the total force on the charges in V. To use it in this case, just use a volume which is a very thin slab of + of area A and neglible thickness (so that you dont have to calculate the thin edges of the slab). Does the direction of F make sense, using what you know about the Coulomb force? Are there any shear forces? Consider a infinitely large parallel plate capacitor, with the lower plate (at z = -d/2) carrying the charge density -, and the upper plate (at z = +d/2) carrying the charge density +. + a) [15 pts] Calculate all nine elements of the Maxwell stress tensor T in the region between the plates, and write out the results in a 3 3 matrix. Also determine the Poynting vector S in the region between the plates. b) [10 pts] Find the force per unit area on the top plate using your T, using the relation: d F = T dA COMO S dr. In this formula, F is the total force on the charges in V. To use it in this case, just use a volume which is a very thin slab of + of area A and neglible thickness (so that you dont have to calculate the thin edges of the slab). Does the direction of F make sense, using what you know about the Coulomb force? Are there any shear forces?