(H) A closed magneticcore is given in Figure P12.14. \text { Let } \phi \text { denotes the flux in the core and } \mu \text { denotes the }

permittivity of the core, find H12, H23, H34, and H41(H12 denotes the magnetic field intensity in the branchPP2 and others are similarly defined). \text { Verify that } \Im=H_{12} l_{2}+H_{23} l_{1}+H_{34} l_{2}+H_{41} l_{1} \text {. } \text { A more general equation is } \Im=\sum H_{m} l_{m} \text { and it is appli- } cable to any closed path.