(Solved): 110. The static magnetic field on the inside part of the surface of an infinite length dielectric ...

110. The static magnetic field on the inside part of the surface of an infinite length dielectric cylinder of circular cross section of radius \( a=4 \mathrm{~cm} \) and of magnetic material with a relative permittivity and permeability of \( \varepsilon_{r}=4, \mu_{r}=9 \) is given by \( \mathbf{H}=\hat{\mathbf{a}}_{\rho} 3+\hat{\mathbf{a}}_{\phi} 6+\hat{\mathbf{a}}_{z} 8 \quad \mathrm{~A} / \mathrm{m} \) at \( \rho=4^{-} \mathrm{cm} \) The cylinder is surrounded on the outside with air. Refer to Figure 3-4 for the cylindrical coordinate system and its units vectors. Determine the: (a) Magnetic flux density on the inside part of the surface of the cylinder \( \left(\rho=4^{-}\right. \) cm; magnetic material). (b) Magnetic field on the outside part of the cylinder surface ( \( \rho=4^{+} \mathrm{cm} \); air). (c) Magnetic flux density on the outside part of the cylinder surface ( \( \rho=4^{+} \mathrm{cm} \); air). Figure P1-10