S is the surface of a lump of magnetic material. a. Lines of B are necessarily continuous across S. b. Some lines of B must be discontinuous across S. c. Lines of H are necessarily continuous across S. d. Lines of H cannot all be continuous across S.

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a and d Explanation: Here we are introducing the properties of magnetic field lines (B), for any magnet, it forms continuous closed loops. This is unlike the electric dipole where these field lines begin from a positive charge and end on the negative charge or escape to infinity. Also, magnetic intensity (H) outside any magnet is H = B/mu_0 and inside the magnet H = B/(mu_0mu_r), where mu_r is the relative permeability of material (magnetic). Magnetic field lines for magnetic field (vecB) is continuous upon a transition through the interface. Also, magnetic intensity (vecH) varies for inside and outside the lump. So, lines of (vecH) cannot all be continuous across S.

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