Magnetism And Matter – NEET UG PhysicsPractice Questions & PYQs

The magnetic torque experienced by a planar coil is given by the relation $\tau = B i A \sin\theta$, where the angle between the magnetic field and the normal to the surface is $90^\circ$ because the field lies directly in the plane of the coil. Substituting the area of an equilateral triangle, $A = \frac{\sqrt{3}}{4} l^2$, into the torque equation yields $\tau = B i \left(\frac{\sqrt{3}}{4} l^2\right)(1)$. Rearranging this expression to isolate the side length gives $l^2 = \frac{4\tau}{\sqrt{3}Bi}$, which simplifies upon taking the square root to $l = 2 \left( \frac{\tau}{\sqrt{3} B i} \right)^{1 / 2}$.

Diamagnetic materials possess completely paired electrons whose orbital and spin magnetic moments completely cancel each other out, resulting in a net magnetic dipole moment of zero. In contrast, paramagnetic materials contain unpaired electrons whose individual magnetic moments do not cancel, giving them a permanent net magnetic dipole moment. Therefore, diamagnetic substances lack intrinsic atomic magnetic dipoles while paramagnetic ones exhibit non-zero magnetic dipole moments.

The oscillation period of a bar magnet in a uniform magnetic field is governed by the formula $T = 2\pi \sqrt{\frac{I}{M B}}$, where $I$ represents the moment of inertia and $M$ is the magnetic dipole moment. Since the moment of inertia is directly proportional to the mass of the magnet, scaling the mass by a factor of four increases $I$ proportionally while the restoring torque properties remain unchanged, preserving simple harmonic motion. Evaluating the square root dependence on mass shows that quadrupling the mass results in the new period becoming twice the original value, yielding a time period of $2T$.

Curie's law establishes that the magnetic susceptibility of certain magnetic materials varies inversely with absolute temperature due to thermal agitation disrupting atomic dipole alignment. As thermal energy increases, random molecular motion counteracts the aligning effect of an external magnetic field, making it progressively harder to magnetize the substance. Mathematically, this inverse relationship means susceptibility is directly proportional to $\frac{1}{T}$.

Diamagnetic substances are characterized by a negative magnetic susceptibility and are weakly repelled by external magnetic fields. When placed in a non-uniform magnetic field, this inherent repulsion creates a net force directed away from regions of high field concentration. Consequently, these materials naturally migrate from areas of higher magnetic flux density to regions where the field is weaker.

The time period of oscillation for a bar magnet suspended in a magnetic field is expressed by the formula $T = 2\pi \sqrt{\frac{I}{M H}}$, where $I$ is the moment of inertia and $M$ is the magnetic moment. When two identical-geometry magnets are aligned with their similar poles on the same side, their magnetic moments add constructively to give a net moment of $3M$ and a combined moment of inertia of $2I$. Reversing the polarity of one magnet causes their moments to oppose each other, reducing the net magnetic moment to $M$ while keeping the total moment of inertia at $2I$. Because the oscillation period is inversely proportional to the square root ofન્દ્ર the net magnetic moment, the smaller resultant moment in the reversed arrangement yields a longer time period, meaning $T_1$ remains less than $T_2$.

A tangent galvanometer operates on the tangent law of magnetism, which relates a known horizontal magnetic field to the deflection produced by an orthogonal current-induced field. When an electric current passes through the circular coil, it creates a magnetic field perpendicular to the Earth's horizontal magnetic component, forcing the magnetized needle to deflect until it aligns with the resultant field vector. This physical setup establishes a direct proportionality governed by the formula $I = K \tan \theta$, allowing the device to accurately measure electric current through the observed angle of deflection.

Magnetic susceptibility describes a material's intrinsic response to an external magnetic field, which originates from distinct atomic-level interactions. In diamagnetic materials, the induced magnetic dipole moments arise from alterations in electron orbital motion under an applied field, an electromagnetic mechanism that remains entirely independent of thermal agitation. Conversely, paramagnetic and ferromagnetic materials rely on permanent atomic magnetic dipoles whose alignment is continuously disrupted by thermal energy, rendering their susceptibility highly temperature-dependent. Thus, diamagnetism alone maintains a constant susceptibility across varying temperature ranges.

The work required to rotate a magnetic dipole from an initial angle to a final angle in a magnetic field is given by the work formula $W = M B (\cos{\theta_1} - \cos{\theta_2})$, while the instantaneous torque acting on it is expressed by the torque formula $\tau = M B \sin{\theta}$. Setting the initial angle to zero and the final angle to 60 degrees simplifies the work expression to $W = MB / 2$. Evaluating the torque at 60 degrees gives $\tau = (\sqrt{3} / 2) M B$, which can be rewritten in terms of work as $\tau = \sqrt{3} W$. Multiplying the given work of $\sqrt{3} \text{ J}$ by $\sqrt{3}$ results in a final torque value of 3 J.

The mechanical torque experienced by a magnetic dipole placed in a uniform external magnetic field is quantified through a vector cross product between the magnetic moment and the magnetic field. When a bar magnet is immersed in such a field, the magnetic forces acting on its opposite poles generate a rotational couple that tends to align its axis with the field lines. The magnitude of this turning effect depends on the strength of both vectors and their relative orientation, while its directional orientation is perpendicular to both. Consequently, the standard vector expression defining this physical phenomenon is given by $\vec{\tau} = \vec{M} \times \vec{B}$.