Electrodynamics Solutions

Electrodynamics Solutions - Electrodynamics Solutions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Electrodynamics Solutions Solution 1 -The AD-axis of the cube has threefold symmetry, i.e. the cube is invariant under rotations by about that axis. 0 120 ± -Hence, the corners , and are equivalent and have the same potential. 1 B 2 B 3 B -Also, the corners , and are equivalent and have the same potential. 1 C 2 C 3 3 C If a current I enters A, then: - A current 3 I circulates through each of the resistors . i AB - A current 6 I circulates through each of the six resistors . j i C B - A current 3 I passes through each of the three resistors . D C j - The potential drop between A and is i B 3 rI . - The potential drop between and is i B j C 6 rI . - The potential drop between and D is j C 6 rI . The potential difference between A and D is: rI rI 6 5 3 1 6 1 3 1 = + + Hence r R 6 5 =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Solution 2 a) Calculate the capacitance of the capacitor. To find the capacitance we would like to find the voltage between the plates for a given charge +Q and Q on the two plates. We can use Gauss’s law (both with and without a dielectric) to find the electric field due to the charge on the plates, using the approximation that there are no end effects. Gauss’s law reads, in general = ε enclosed Q S d E r r where o κε = is the general form of the electric permittivity in the presence of a dielectric (note that in free space κ = 1). If we use a pill-box shaped Gaussian surface with end area A and with one end below the bottom plate, which is charged to Q, and the other end inside the dielectric, then Gauss’s law gives us , ' ' ' A A Q A Q A E S d E enc d d εε σ = = = = r r
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

Electrodynamics Solutions - Electrodynamics Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online