The diagram below shows an ohmic film with conductivity , thickness d, infinite length, and semi-infinite width.

The diagram below shows an ohmic film with conductivity σ, thickness d, infinite length, and semi-infinite width. A total current I enters the film at the point A through a line contact (modeled as a half-cylinder with negligible radius) and exits the film similarly at the point B. The potential difference V_D − V_C between the contact at C and the contact at D determines the resistance R_AB,CD. The contact separations are a, b, and c, as indicated.

(a) Show that the electrostatic potential produced at point C by the current injected at point A is

(b) Prove that

Transcribed Image Text:

A B C C V D d