Q4. Assertion: the net magnetic flux through a closed surface that encloses one pole of a bar magnet is zero. Reason: magnetic field lines are continuous closed loops that run through the magnet itself. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: every line that leaves the surface outside the magnet enters it again through the magnet (NCERT pages 137 and 142).
Q5. A closed cylinder of cross-section 4.0 × 10−3 m stands with its axis along a uniform field of 0.50 T. Find the flux through each end, through the curved side and through the whole surface.
Through the end the field enters, −BA = −0.50 × 4.0 × 10−3 = −2.0 × 10−3 Wb; through the other end, +2.0 × 10−3 Wb; through the curved side, zero, since B is along the surface. The total is zero (NCERT Eq. (5.6), page 142).
Q6. Field lines are drawn leaving an upper plate from both its faces, spreading out above it and bulging outwards below it, and converging from all sides onto a lower plate. Can these be magnetic field lines? (NCERT Example 5.3(f))
No. The lines all leave one plate, so a closed surface round that plate would have a net outward flux, which is impossible for B. They are the electric field lines between a positively and a negatively charged plate (NCERT page 144).
Q7. Does a bar magnet exert a torque on itself due to its own field? Does an element of a current-carrying wire feel a force from the field it produces itself? Does it feel a force from other elements of the same wire? (NCERT Example 5.4(c))
A static isolated bar magnet has no net torque on itself. In the ideal point-element model used here, omit the element’s own singular field when evaluating its Lorentz force; other elements of the wire can exert forces on it (NCERT page 145). For an ideal straight filament their contribution at another collinear element is zero. A real wire of finite cross-section can have internal magnetic pinch forces, so this is not a claim that all self-stress vanishes; radiation reaction is outside this static model.
Q8. A magnet has a narrow gap between its N and S pole pieces. The field lines in the gap are drawn perfectly straight, stopping sharply at the edges. Right or wrong? (NCERT Example 5.3(g))
Wrong. Fringing at the gap edges is inevitable. In a current-free static gap, a sharp boundary between a uniform field and zero field would give non-zero circulation around a small loop crossing that boundary, contrary to Ampere’s law (NCERT page 144). Electric fields fringe too, but the corresponding electrostatic reason is zero circulation of E, not Ampere’s law.