Electronic – Avoid inductive coupling on two near coils

I think you are looking for Ampere's law and Faraday's law, parts of Maxwell's equations.

For a distance D between coils much greater than the coil diameter, The voltage induced on the second coil from a given current on the input coil is something like

• Vout = 2 π f N S Bo cos b,

where

• f = carrier frequency of transmitted signal in Hz
• N = number of turns in the receiving output coil
• S = area of output loop in m^2
• Bo = strength of the arrival magnetic field
• b = angle of the output coil away from "axis pointing directly at input coil"

and in turn,

• Bo = μ0 I N R^2 cos a / ( 2( R^2 + D^2 )^3/2 ),

where

• μ0 = the universal permeability of free space
• I = current in input wire
• N = number of turns in the transmitting coil
• R = radius of transmitting coil
• D = distance between the coils
• a = angle of the transmitting coil axis away from "axis pointing directly at output coil"

At long distances, the magnetic field (and hence the produced voltage) drops off with D^(-3).

• "Microchip AN678: RFID Coil Design"

• "Microchip microID(R) 125 kHz RFID System Design Guide"

The fuse F1 will protect V1 and V2 against SW1 and SW2 being closed simultaneously. Both switches closed together will cause a short circuit of the 2 voltage sources - depending on what these voltage sources are the current spike caused by a short circuit could be catastrophic.