Magnetism and Matter links microscopic magnetic moments to macroscopic fields and material response (diamagnetism, paramagnetism, ferromagnetism). Mastery of this chapter is essential for CBSE board problems on magnetisation, bound currents, B–H relations and for competitive exams (JEE/NEET) where multi-step reasoning about fields in media, force on dipoles in non‑uniform fields and energy in magnetic systems is frequently tested.
This set emphasises quantitative skill, graph/data interpretation and conceptual pitfalls (e.g. bound vs free currents, demagnetizing fields, hysteresis losses). Expect questions that combine Ampère’s law with magnetisation, use or , and require interpreting hysteresis or – curves — all typical of board and entrance-exam style reasoning.
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Marking Scheme
Q1. A long solenoid of length has turns and carries a current . A soft-iron core with relative permeability is fully inserted. Neglect end effects; calculate the magnetic induction inside the solenoid.
Q2. Assertion (A): A very long solid cylinder of radius uniformly magnetised along its axis with produces a uniform magnetic induction inside and (to a good approximation) negligible magnetic field outside.
Reason (R): The uniform magnetisation is equivalent to an azimuthal bound surface current density , which produces the same inside/outside field pattern as an ideal infinite solenoid.
Q3. A small magnetic dipole of magnetic moment magnitude is oriented along the axis and placed at in a magnetic field (with in metres). Calculate the magnitude and direction of the force on the dipole.
Q4. Three ferromagnetic samples A, B and C are cycled by the same alternating magnetising field and produce the following qualitative hysteresis loops ( vs ): loop A is very narrow with very small coercivity and small remanence ; loop B has moderate and ; loop C is wide with large and large . Which assignment of practical applications is most appropriate?
Q5. Assertion (A): A freely movable diamagnetic rod placed in a non‑uniform external magnetic field moves toward the region of weaker magnetic field.
Reason (R): The induced magnetic moment in a diamagnetic material is opposite to the applied field, so the system’s magnetic potential energy is minimised when the rod moves to a region of smaller field.
Q6. A toroidal core has mean radius and cross‑sectional area . It has turns and carries a current . The core’s relative permeability is . Assuming the magnetic field is confined to the core, calculate the total magnetic energy stored in the toroid. (Use and for the mean path.)
Q7. A long solenoid produces an almost uniform internal magnetic field directed along and negligible field outside. A small bar magnet with magnetic moment is placed just outside the solenoid on its axis where and is free to move along . If is aligned along , which of the following describes the initial motion of the magnet?
Q8. Assertion (A): For a uniformly magnetised solid sphere with magnetisation , the internal magnetic field intensity is (the demagnetising field).
Reason (R): Bound surface currents on the sphere produce, inside the sphere, a uniform field that opposes and has magnitude .
Q9. A qualitative plot of magnetisation versus applied field at room temperature for three materials I, II and III is described as follows: I is a straight line with a small negative slope through the origin; II is a straight line with a small positive slope through the origin; III shows a very steep initial rise and then saturates at high (nonlinear). Identify I, II and III respectively.
Q10. A ferromagnetic sample's hysteresis loop in the – plane is approximately rectangular and symmetric about the origin with coercive field and remanent induction . Using this rectangular approximation, estimate the magnetic energy loss per cycle per unit volume in . (Use .)