DC signaling in conducting media

The electric field produced by the dc current between two spheres is calculated and expressed in terms of input power. The attenuation between these spheres and a pair of receiving spheres considered as a four terminal network is found to beP₂/P₁ = l₁²l₂²a₁a₂/16r⁶, wherea₁is the radius of the transmitting spheres separated by a distancel₁apart,a₂is the radius of the receiving spheres separated by a distancel₂, andris the distance between transmitter and receiver all in the same units. This equation applies when the line joining the receiving spheres is parallel to the line joining the transmitting spheres and perpendicular to the direction of propagation. For colinear spheres,P₂/P₁is four times as great but other factors combine to counteract this apparent advantage. The transient responses to a unit step and a unit pulse are calculated and presented as curves. The minimum practical pulse duration for the former configuration ist₀ = σμ r²/8, where the conductivity and permeability all in inks units. A pulse of the same length is more smeared in the colinear direction and reduced in amplitude by a factor of approximately three, and power by a factor of nine more than counteracting the favorable factor of four for the steady-state condition for colinear spheres.