An iron tor suports `N = 500` turns. Find the magnetic field energy if a current `I = 2.0 A` preoduces a magnetic flux across the tore's cross-section equal to `Phi = 1.0 mWb`.

Explanation

To find the magnetic field energy we recall that the flux varies lineraly with current. Thus, when the flux is `Phi` for current `i`, we can write `Phi = A i`, The total energy inclosed in the field, when the current is `I`, is
`W = int xi I dt = int N (d Phi)/(dt) i d t`
`= int N d Phi i = int_(0)^(I) N A i di = (1)/(2) N A I^(2) = (1)/(2) N Phi I`
The characteristic factor `(1)/(2)` appears in this way.