gives: Where L is just a linearity constant called the inductance measured in Henry. Now that the power is found, all that is left to do is fill in the work equation to find the work. As said earlier the work has to be equal to the energy stored in the field. This entire calculation is based on a single looped wire. For wires which are looped multiple times the Induction L increases, as L is simply defined as the ratio between the voltage and rate of change of the current. In conclusion the stored energy in the coil is equal to: Where E = energy measured in joules L = inductance measured in henries I = current measured in amperes Now let's consider a cylindrical coil with conductors of a rectangular cross section. The mean radius of coil is R. a and b are width and depth of the conductor. f is called form function which is different for different shapes of coil. ξ (xi) and δ (delta) are two parameters to characterize the dimensions of the coil. We can therefore write the magnetic energy stored in such a cylindrical coil as shown below. This energy is a function of coil dimensions, number of turns and carrying current. Where E = energy measured in joules I = current measured in amperes f(ξ,δ) = form function, joules per ampere-meter N = number of turns of coil Solenoid versus toroid Besides the properties of the wire, the configuration of the coil itself is an important issue from a mechanical engineering aspect. There are three factors which affect the design and the shape of the coil - they are: Inferior strain tolerance, thermal contraction upon cooling and Lorentz forces in a charged coil. Among them, the strain tolerance is crucial not because of any electrical effect, but because it determines how much structural material is needed to keep the SMES from breaking. For small SMES systems, the optimistic value of 0.3% strain tolerance is selected. Toroidal geometry can help to lessen the external magnetic forces and therefore reduces the size of mechanical support needed. Also, due to the low external magnetic field, toroidal SMES can be located near a utility or customer load. For small SMES, solenoids are usually used because they are easy to coil and no pre-compression is needed. In toroidal SMES, the coil is always under compression by the