fig1 illustrates an isometric simplified representation of a deicing system 10 within a fluid receptacle 12 according to an embodiment of the present invention . the fluid receptacle 12 includes lateral walls 14 integrally formed with a base 16 . a fluid retention cavity 18 is defined between the lateral walls 14 and the base 16 . the fluid receptacle 12 may be a birdbath , a livestock water tank , or various other structures that are designed to retain fluid . fluid , such as water 20 , may be retained within the fluid receptacle 12 . the deicing system 10 may include a flotation member 22 connected to a heating element 24 ( such as a heater coil ), a capacitor plate ( not shown in fig1 ) and an insulated cord 26 that supplies power from a power source 28 , such as a standard wall outlet , to the deicing system 10 . the deicing system 10 may also include a sensing unit 30 , such as a microchip having a central processing unit , which is programmed to control operation of the deicing system 10 , in communication with the capacitor ( as discussed below ). alternatively , the deicing system 10 may not include a flotation member 22 . optionally , the sensing unit 30 may be remotely located from the deicing system . additionally , instead of the cord 26 and the power source 28 , the deicing system 10 may be battery or solar powered . the flotation member 22 may be an air - filled bladder , styrofoam , rubber , or various other materials that provide buoyancy to the deicing system 10 . the flotation member 22 ensures that the deicing system 10 floats within the fluid receptacle 12 when a sufficient amount of water 20 is retained therein . the heating element 24 operates to heat the water 20 within the fluid receptacle 12 so that the water 20 does not freeze . as discussed below , when fluid recedes , evaporates , drains , or is otherwise removed from the fluid receptacle 12 such that fluid is no longer proximate the capacitor ( not shown in fig1 ), the sensing unit 30 acts to deactivate the heating element 24 so that the heating element 24 does not damage the fluid receptacle 12 , or otherwise pose a safety hazard . fig2 illustrates a lateral view of the deicing system 10 . as mentioned above , the deicing system 10 includes the flotation member 22 , the capacitor plate 32 , and the heating element 24 . a conduit 34 passes through the flotation member 22 and allows power to be delivered from the cord 26 to the heating element 24 . the sensing unit 30 is shown on top of the flotation member 22 . however , the sensing unit 30 may be disposed within the flotation member 22 , on or within the capacitor plate 32 or a separate support , or mounted to the heating element 24 . fig3 illustrates a schematic representation of the sensing unit 30 . the sensing unit 30 includes a main body 31 housing a processor 33 operatively connected to a sensing circuit 35 , which may include the capacitor plate 32 . referring again to fig2 , the capacitor plate 32 is secured to an underside of the flotation member 22 . for example , the capacitor plate 32 may be fastened to the flotation member 22 , or a plate , sheet or the like that supports the flotation member 22 , through adhesives or bonding material . optionally , the capacitor plate 32 may secure to the flotation member through screws , bolts , or the like . as shown in fig2 , the capacitor plate 32 is approximately the same length and width as the heating element 24 . in particular , the capacitor plate 32 may have the same , or larger , perimeter as the heating element 24 , such that the length and width dimensions of the capacitor plate 32 are similar , or exactly the same , as that of the heating element 24 . further , the capacitor plate 32 may be positioned directly above , and in alignment with , the heating element 24 so that , in general , the outer boundaries of the heating element 24 do not extend past the outer x - y plane ( relative to the deicing system 10 ) envelope of the capacitor plate 32 . that is , the footprint of the capacitor plate 32 is the same , or roughly the same , as that of the flotation member 22 . fig6 illustrates a top isometric simplified representation of the heating element 24 . as shown in fig6 , the heating element 24 , much like the capacitor plate 32 ( shown in fig2 ), has a length “ l ”, a width “ w ”, and a height “ h ”. the outer length - width envelope of the heating element 24 is defined by plane ab , plane bc , plane cd , and plane da , which extend through respective sides of the heating element 24 . referring again to fig2 , a post 36 extends from , or through , the capacitor plate 32 and secures the heating element 24 to the capacitor plate 32 and / or the flotation member 22 . various other structures may be used to secure the heating element 24 to the flotation member 22 , such as lateral clamps , locks , or the like . the heating element 24 may be secured to a support bracket that also secures to the flotation member 22 . as shown in fig2 , a clearance gap 38 is defined between the capacitor plate 32 and the heating element 24 . fluid , such as air or water , may flow through the gap 38 between the capacitor plate 32 and the heating element 24 . alternatively , the heating element 24 may be directly attached to the capacitor plate 32 such that the capacitor plate 32 directly abuts a top or bottom surface of the heating element 24 . fig4 illustrates a lateral cross - sectional view of the heater coil 24 . the heating element 24 includes a metal sheath 40 having a central core 42 that may be packed with magnesium oxide ( mgo ), which may serve as a thermal conductor and electrical insulator . an electrical insulating compound 44 is disposed within the central core 42 . additionally , a heater wire 46 is disposed within a central portion of the electrical insulating compound 44 . instead of using a separate capacitor plate , such as capacitor plate 32 ( shown , for example , in fig2 ), the metal sheath 40 of the heating element 24 may be used as a capacitor . referring to fig1 - 4 , presence of water around the heating element 24 may be detected by measuring capacitance . the capacitance of a plate , or set of plates , is determined through equation ( 1 ): where c is the value of capacitance , k is the dielectric constant , ε 0 is the permittivity constant with a value of 8 . 85 × 10 − 12 farads / meter , and l depends upon the geometry of the capacitor and has dimensions of length . for a parallel plate capacitor , l has the value a / d , where a is the area of each plate and d is the distance between the plates . the dielectric constant k depends upon the material adjacent to the capacitor . for instance , air has a dielectric constant of 1 , pyrex glass has a dielectric constant of 4 . 5 , while polystyrene plastic has a dielectric constant of 2 . 6 . the dielectric constant of water is 78 . thus , the capacitance changes by a factor of 78 for a plate capacitor , depending on whether air or water is the dielectric material . such change in capacitance provides a determination as to whether water or air is contained in a receptacle on which the capacitor is mounted . the relationship between capacitance , charge and voltage is given by equation ( 2 ), set forth below : where q is the charge on the capacitor and v is the voltage across the terminals . a change in capacitance is seen as a change in charge for a given voltage when the dielectric material changes . fig5 illustrates a simplified circuit diagram 50 of the sensing unit 30 ( shown in fig1 - 3 ), according to an embodiment of the present invention . the circuit diagram 50 is simplified for the sake of clarity . the sensing unit 30 shown in fig3 may include a circuit including the elements shown in fig5 . moreover , the sensing unit 30 may include additional electrical components , such as additional resistors , capacitors , and the like . in order to observe a change in capacitance , one may connect a capacitor 52 , such as the capacitor plate 32 ( shown in fig2 ) or the metal sheath 40 ( shown in fig4 ), in series with a resistor 54 to form an rc circuit . connecting the circuit to a battery 56 causes current to flow through the resistor 54 and charge the capacitor 52 . instead of the battery 56 , the rc circuit may be connected to a source of alternating current , such as provided through a standard wall outlet . the rate at which the charge on the capacitor 52 increases is given by equation ( 3 ): where q is once again the charge , v 0 is the battery voltage , r is the resistance of the resistor , and c is the capacitance of the capacitor . the value rc is called the time constant of the circuit . because , v = q / c , the voltage v c across the capacitor is given by equation ( 4 ) set forth below : thus , the voltage across the capacitor 52 increases exponentially as a function of time . by replacing c in the equation ( 4 ) with a higher value , such as would occur with an increase in the dielectric constant , the time constant rc changes accordingly , and the capacitor 52 therefore takes longer to charge . the change in the time constant is directly proportional to the change in capacitance . a detected change in capacitance may be used to deactivate the heating element 24 . the presence of air and water around the heating element 24 may , alternatively , be detected by sensing changes in resistivity . the relationship between voltage , current , and resistance is given by equation ( 5 ), which is ohm &# 39 ; s law : where v is the voltage , i is the current in amperes , and r is the resistance in ohms . for a resistor , however , the resistance can be expressed in terms of resistivity “ p ” by equation ( 6 ): where a is the cross - sectional area of the resistor , and l is the length of the resistor . the resistivity , in turn , is dependent upon temperature , as given by equation ( 7 ): where t is the temperature , p 0 is the resistivity at temperature t 0 , and α is the temperature coefficient of resistivity . for a material such as nickel , the temperature coefficient of resistivity is approximately 6 . 0 × 10 − 3 k − 1 . using t 0 = 298k ( room temperature ) and t = 506k ( the temperature at which paper ignites ) with respect to equation ( 7 ), p =( 2 . 2 ) p 0 . thus , the resistivity more than doubles as the resistor is heated to 506k . however , for a resistor that is submerged in water at room temperature , the water absorbs the heat from the resistor , and the resistance is r = p 0 l / a . if , however , part of the resistor ( e . g ., 1 / 20 of the length ) is protruding from the water and allowed to heat up to 506k , the resistance increases , such as by six percent ( 6 %). this change in resistance may be detected and used to deactivate the heating element 24 . referring to fig1 - 5 , the sensing unit 30 may be mounted to the exterior of a container , or within a non - metallic container in which the dielectric constant of the capacitor plate 32 is determined by the presence of air or water adjacent to the capacitor plate 32 . optionally , the sensing unit 30 may be separated from the capacitor plate 32 by a non - metallic substance . as shown in fig2 , for example , the capacitor plate 32 is secured to the underside of the flotation member 22 . as the water 20 within the fluid receptacle 12 decreases , the deicing unit 10 may come to rest against an obstacle that tips the deicing unit 10 such that part of the heating element 24 is exposed to air . because the footprint of the capacitor plate 32 is approximately the same as that of the heating element 24 , if a portion of the heating element 24 is exposed to air , a corresponding portion of the capacitor plate 32 will also be exposed to air . for example , if an end 60 of the heating element 24 is exposed to air , an end 62 of the capacitor plate 62 will also be exposed to the air . optionally , if the metal sheath 40 of the heating element 24 is used as the capacitor plate , changes in capacitance are detected in a similar way . as shown in fig4 , the metal sheath 40 surrounds the heater wire 46 . whether the capacitor plate 32 or the metal sheath 46 is used to detect capacitance , the sensing unit 30 receives a capacitance change signal from the capacitor plate 32 , thereby sensing a change in capacitance , as discussed above . the processing unit 33 ( shown in fig3 ) may then send a deactivation signal to the heating element 24 based on the sensed change in capacitance , thereby turning the heating element 24 off . alternatively , the resistance of the metal sheath 40 of the heating element 24 itself may be measured by the sensing unit 30 to determine if the resistivity of any section of the sheath 40 or the heating element 24 has increased , thereby signaling a hot spot . as discussed above , the resistivity may be determined by measuring the value of resistance with the known value when the deicing system 10 is operating properly . the sensing unit 30 may sense an increase in resistance , and operate to deactivate the heating element 24 in response to the sensed increase in resistance . thus , embodiments of the present invention provide a safe and reliable system and method of deactivating a deicing system within a fluid receptacle . embodiments of the present invention provide a deicing system that automatically deactivates a heater coil based on a detected physical change , such as a change in capacitance or resistivity . further , embodiments of the present invention do not rely on a thermostat in order to deactivate the heater coil . while the invention has been described with reference to certain embodiments , it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the invention . in addition , many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from its scope . therefore , it is intended that the invention not be limited to the particular embodiments disclosed , but that the invention will include all embodiments falling within the scope of the appended claims .