Magnetism and Matter is central to understanding how magnetic materials respond to external fields, how demagnetizing effects modify internal fields, and how forces/torques arise due to non-uniform magnetization. These concepts are frequently asked in CBSE boards and are also important for JEE/NEET because they connect fundamental field theory ( ) with practical phenomena like magnetic levitation, solenoid/magnetic-circuit behavior, and dipole forces.
20
Minutes
15
Questions
1 / -0
Marking
Q1. A rectangular coil with turns and sides and carries current . It is placed in a uniform magnetic field such that the plane of the coil makes an angle with . The magnitude of the torque on the coil is
Q2. A long solenoid has turns per unit length and cross-sectional area , and it carries a steady current . A linear magnetic rod (same cross-section) of susceptibility is inserted so that a length of the rod lies inside the solenoid. Neglecting end effects, the magnitude of the force tending to pull the rod further into the solenoid is
Q3. The axial magnetic field of a circular coil on its axis is given by , where the coil centre is at . A small magnetic dipole of moment is placed at on the axis. What is the direction of the net force on the dipole?
There is no net axial force; only a torque tends to align the dipole
Net force along (away from the coil centre)
Net force is zero because has a stationary point at
Net force along (towards the coil centre at )
Q4. A small spherical sample of a linear magnetic material with magnetic susceptibility is placed in an initially uniform external magnetic field (directed along ). Using the demagnetizing factor for a sphere (), the magnetic induction at the centre of the sphere equals
Q5. A small spherical paramagnetic particle (radius , density , susceptibility ) is placed at in a vertical magnetic field with . For a small particle the magnetic force may be approximated by . The minimum required to levitate the particle (i.e. at ) is closest to:
Q6. A long solenoid of length has turns and carries a steady current . It is completely filled with a linear magnetic material of susceptibility . Using and , the magnitude of magnetization of the material is:
Q7. A small spherical sample of linear paramagnetic material with susceptibility is placed in a uniform magnetic induction produced in vacuum. For a sphere the demagnetizing factor is . Taking the demagnetizing field into account, the magnetic induction inside the sphere is closest to:
Q8. A ferromagnetic core of mean length and cross-sectional area has relative permeability . An air gap of length is introduced. A coil of turns carrying current is wound on the core. Neglect fringing. The magnetic flux in the core is approximately:
Q9. A long solenoid of length and turns carries current . Half its length is filled with a linear magnetic material of relative permeability , the other half remains vacuum. Using the magnetic-circuit approximation (neglect fringing), the ratio equals:
Q10. A small spherical paramagnetic particle (radius , density , susceptibility ) is placed at in a vertical magnetic field with . For a small particle the magnetic force may be approximated by . The minimum required to levitate the particle (i.e. at ) is closest to:
Q11. A long solenoid (length ≫ radius) has and carries current . A linear magnetic material with susceptibility completely fills the solenoid. The magnetic induction inside the filled solenoid is approximately:
Q12. A very long solenoid has and carries current . A paramagnetic rod of cross-sectional area and susceptibility is partially inserted so that a length is inside. Assuming the solenoid field is and unaffected by insertion, the magnitude of the force pulling the rod further into the solenoid is . The numerical value of is closest to:
Q13. A small sphere made of a linear magnetic material with susceptibility is placed in a uniform external magnetic field . For a sphere the demagnetizing factor is . Using the relation , the magnetization inside the sphere is:
Q14. An infinitely long cylindrical rod of radius is uniformly magnetized along its axis: . Neglect end effects. Which of the following gives the magnetic induction (in vacuum) inside () and outside () the cylinder?
Q15. A circular coil of radius carries current . The magnetic field on its axis a distance from the centre is . A small magnetic dipole of moment (aligned along the axis) is placed at the centre and is free to move along the axis. For small axial displacement the axial force is . Which statement about the stability of the centre is correct?
The centre is a stable equilibrium if points in the same direction as the coil's field (parallel to ); it is unstable if is anti-parallel.
The centre is stable only if is anti-parallel to the coil's field; unstable if parallel.
The centre is neutrally stable for any orientation of .
The centre is always unstable because regardless of the sign of .