embodiments of a power transmission system employ a coaxial cable for the transmission of electrical power . by this means , the efficiency of the operation is enhanced , particularly in those special applications where direct current is now used . the outstanding feature of embodiments of the power transmission system is that it is compatible with the existing power grid . in one embodiment of a power transmission system , 60 cycles per second , single - phase , alternating current is transmitted by the coaxial cable . one pole of the power supply leads to the central wire of the cable , and the other pole is attached to the conductive tube encasing the central wire . the electric current which travels in the central wire at all times is equal to but moving in the opposite direction from the current flowing in the outer shell . thus , the electromagnetic field generated by one current cancels the field generated by the other current . the net result is that the cable has zero electromagnetic field strength , and losses due to radiation are eliminated . the phenomenon can better be visualized by referring to fig4 . the sinusoidal curve representing the voltage in lead 1 is completely balanced by a similar curve for lead 2 . sometimes this arrangement is referred to as a two - phase system comprising two equal voltages oppositely directed . the more correct terminology , however , is single - phase . since the power grid is universally three - phase , provision must be made to convert this electricity to single - phase in order to transmit it by a coaxial cable . conceptually this conversion is shown in the figures and description herein . three - phase power can be used in a motor to drive a single - phase generator . the cost and added complexity of this scheme , however are a disadvantage . embodiments of conversion mechanisms for a power transmission system envisions the use of a transformer of unique design to convert three - phase power to single - phase electricity . such a transformer is illustrated in fig1 . the transformer is in the shape of a torus with a vertical chord passing through the axis . both torus and chord are made from magnetic material such as iron . the primary winding of the transformer is coiled about the torus with both ends attached to each other . the power leads to the primary winding , shown as a , b and c , are attached at equidistant points on the torus or 120 ° apart on the circle . one lead , a , is located at the top of the torus , just above one end of the chord . the secondary winding is coiled about the chord . the two ends of this winding are attached to the take - off leads 1 and 2 . the electric power profiles are shown in fig3 and 4 . the three - phase power supply is shown as three sinusoidal curves a , b and c in fig3 . the output voltage 1 and 2 are shown as two sinusoidal curves in fig4 . the frequency of the output is the same as the input , and there is no phase shift . another transformer arrangement is shown in fig2 . the transformer cores and windings are identical to the features shown in fig1 , but the leads are located at different points . in this particular case , lead a is shifted 30 ° from the vertical . the other leads band are likewise rotated 30 °. the effect of the changes in lead location is quite interesting . the voltage outputs for the transformer are shown in fig5 . noticeably there is a phase shift in the secondary voltage . while this shift will have no effect on the power transmission in the coaxial cable , it can cause problems for reconnecting the cable to the grid . at the other end of the coaxial cable , where it is reconnected to the grid , single - phase current must be converted back to three - phase current . this conversion is achieved using the same transformer but with reverse connections . the winding on the chord now becomes the primary . materials of construction are important . while standards for such materials are disclosed in prior art , the size of the equipment will place extra demands on the conductors and insulation . in cases where heavy loads are contemplated , a water jacket can be used to cover the coaxial cable . applications for the power transmission systems , associated transformers , and methods of use are virtually unlimited . whether used for transmitting power long distances , distributing electricity in urban areas or serving residential communities , a coaxial cable can provide superior performance under varying conditions . in order to determine the voltage profile of the secondary current , a series of calculations was made . as an example of these calculations , the values for voltage in the primary winding of the transformer of fig1 was taken at time t when phase a was in the 60 ° position . from fig3 , the voltage at contact point a equals + 0 . 54 volts , at b + 0 . 54 volts and at c − 1 . 0 volts . again looking at fig1 , the magnetic flux was determined for the left side of the torus as follows . the current in the winding between a and b was zero . the current between b and c was proportional to + 0 . 54 −(− 1 . 0 ) or 1 . 54 and in a clockwise direction . the magnetic flux in the segment of the torus from b to its lowest point was 0 . 5 n ( 1 . 54 ) or 0 . 77 n where n is the number of windings between each primary contact . thus , the total flux in the left side of the torus was 0 . 77 n . using the same reasoning , the magnetic flux in the right side of the torus was determined to be 0 . 77 n . because the current on the left side of the torus rotates in the same direction as the current on the right side , both the magnetic fields on the left side of the torus and the right side are pointing in the same direction , that is , the north poles are both up . as a result , the magnetic fluxes are additive and together equal the flux in the vertical cord , namely , 1 . 54 n . if the number of turns of the secondary winding is equal to n , the voltage across the terminals 1 and 2 is equal to 1 . 54 . thus , the potential of terminal 1 is + 0 . 77 volts and at terminal 2 , − 0 . 77 volts . table 1 gives the results for the calculation made for the transformer shown in fig1 . likewise table 2 produces values for the transformer of fig2 . the results for both transformers are shown graphically in fig4 and 5 . the previous detailed description is of a small number of embodiments for implementing the systems and methods for creating power transmission systems and is not intended to be limiting in scope . the following claims set forth a number of the embodiments of the systems and methods for creating power transmission systems and the systems of power transmission systems disclosed with greater particularity .