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7-11. Two cylindrical copper electrodes of radius a are oriented normal to a silicon disk of thickness 8, and are separated axially by the distance 6. The electrodes are embedded in the disk to the depth 8; in other words, they go completely through the disk. The lateral dimensions of the disk are large com- pared with b, and may bc considercd infinite. Taking the conductivity of silicon to be g, fînd the current between tihe eiectrodes when iheir poieutiai difference is AU.

7-11. Two cylindrical copper electrodes of radius a are oriented normal to a silicon disk of thickness 8, and are separated axially by the distance 6. The electrodes are embedded in the disk to the depth 8; in other words, they go completely through the disk. The lateral dimensions of the disk are large com- pared with b, and may bc considercd infinite. Taking the conductivity of silicon to be g, fînd the current between tihe eiectrodes when iheir poieutiai difference is AU.

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FOUNDATIONS OF ELECTROMAGNETIC THEORY (REITZ) TOPIC: ELECTRIC CURRENT Solve step by step using the theory of the book 7-11. Two cylindrical copper electrodes of radius a are oriented normal to a silicon disk of thickness 8, and are separated axially by the distance 6. The electrodes are embedded in the disk to the depth s; in other words, they go completely through the disk. The lateral dimensions of the disk are large com- pared with b, and may bc considercd infinite. Taking the conductivity of silicon to be g, fînd the current between the eiectrodes when iheir poviential differencve is AU. 7.11 I = ngs A/cosh- (b/2a) ans.
Transcribed Image Text:FOUNDATIONS OF ELECTROMAGNETIC THEORY (REITZ) TOPIC: ELECTRIC CURRENT Solve step by step using the theory of the book 7-11. Two cylindrical copper electrodes of radius a are oriented normal to a silicon disk of thickness 8, and are separated axially by the distance 6. The electrodes are embedded in the disk to the depth s; in other words, they go completely through the disk. The lateral dimensions of the disk are large com- pared with b, and may bc considercd infinite. Taking the conductivity of silicon to be g, fînd the current between the eiectrodes when iheir poviential differencve is AU. 7.11 I = ngs A/cosh- (b/2a) ans.
Consider a wave in one dimension incident from the left, where V = 0, with positive energy, momentum along the z axis of p = along the z axis. This is reflected and transmitted at z = becomes Vo > E + m for z > 0. The momentum of the transmitted wave is q = V(E – Vo)² – m². Write the general form of the reflected and transmitted waves. VE - m? and spin up O where the potential 0, show that the transmitted and From the continuity of the wave at z = reflected waves have no component with spin down, and show that the ratio of the transmitted wave amplitude to incident wave amplitude is 2/(1 + r), and the ratio of the transmitted current J, to the incident current J; is 4r E + m where рЕ— Vo + m Show that this is negative, and hence that the reflected current must be greater (1 +r)2 | than the incident current.
Transcribed Image Text:Consider a wave in one dimension incident from the left, where V = 0, with positive energy, momentum along the z axis of p = along the z axis. This is reflected and transmitted at z = becomes Vo > E + m for z > 0. The momentum of the transmitted wave is q = V(E – Vo)² – m². Write the general form of the reflected and transmitted waves. VE - m? and spin up O where the potential 0, show that the transmitted and From the continuity of the wave at z = reflected waves have no component with spin down, and show that the ratio of the transmitted wave amplitude to incident wave amplitude is 2/(1 + r), and the ratio of the transmitted current J, to the incident current J; is 4r E + m where рЕ— Vo + m Show that this is negative, and hence that the reflected current must be greater (1 +r)2 | than the incident current.
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