Magnetism And Matter – NEET UG PhysicsPractice Questions & PYQs

The apparent dip angles in two mutually perpendicular planes are related to the true dip angle $\theta$ and the angle $\alpha$ made by one of the planes with the magnetic meridian through the expressions $\tan \theta_1 = \frac{\tan \theta}{\cos \alpha}$ and $\tan \theta_2 = \frac{\tan \theta}{\sin \alpha}$. Inverting these equations gives the corresponding cotangents as $\cot \theta_1 = \cot \theta \cos \alpha$ and $\cot \theta_2 = \cot \theta \sin \alpha$. Squaring both expressions and adding them together eliminates the angle $\alpha$ using the fundamental trigonometric identity $\cos^2 \alpha + \sin^2 \alpha = 1$, resulting in the relationship $\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2$.

The work done in rotating a magnetic dipole from stable equilibrium to an angle $\theta$ is given by $W = MB(1 - \cos \theta)$, which for $\theta = 60^\circ$ becomes $W = MB(1 - \cos 60^\circ) = \frac{MB}{2}$, establishing that $MB = 2W$. The restoring torque acting on the magnet at this new position is expressed as $\tau = MB \sin \theta$, and substituting $\theta = 60^\circ$ along with the relation for $MB$ into the torque formula yields $\tau = 2W \sin 60^\circ = 2W \left(\frac{\sqrt{3}}{2}\right) = \sqrt{3}W$.

Magnetic susceptibility measures the degree of magnetization of a material in response to an applied magnetic field. For diamagnetic materials, the orbital motion of electrons creates induced magnetic moments that oppose the external field, leading to a negative susceptibility value. In contrast, paramagnetic and ferromagnetic materials possess positive susceptibility because their internal moments align parallel to the external field.

The torque acting on a current-carrying coil placed in a uniform magnetic field is expressed by the formula $\tau = NIAB \sin \theta$. The surface area of the coil is calculated by multiplying its length and width, giving 0.012 square meters. Given that the plane of the coil is inclined at 30 degrees to the magnetic field, the angle between the magnetic moment vector and the field vector is given by the equation $\theta = 90^\circ - 30^\circ = 60^\circ$. Substituting the number of turns, current, area, magnetic field strength, and the sine of 60 degrees into the formula yields a torque of 0.20 Nm.

Net magnetic dipole moment is determined by vectorially combining individual magnetic moments $\vec{m}$ based on their relative orientations. For configuration C, the resulting vector sum yields $M_3 = m\sqrt{2+\sqrt{3}}$, which is greater than the alternative configurations that produce values like $m\sqrt{3}$ or cancel out completely to zero.

The magnetic force experienced by a magnetic pole in a field is given by the relation $F = mB$, while the magnetic moment of a bar magnet is defined as $M = mL$. Rearranging the force equation yields the expression for pole strength as $m = \frac{F}{B}$, and substituting this into the magnetic moment equation gives $M = \frac{F}{B} \times L$. Isolating the length $L$ results in the final formula $\frac{MB}{F}$.

The magnetic dipole moment of a bar magnet is determined by multiplying its pole strength by the straight-line distance separating its north and south poles. For the initial straight magnet, the magnetic moment is expressed as $M = m l$, utilizing the pole strength $m$ and the total length $l$. When this magnet is curved into an arc, its length forms an arc of radius $r$ with a subtended angle of $\frac{\pi}{3}$ radians, establishing the relation $l = \frac{\pi}{3} r$ or $r = \frac{3l}{\pi}$. The effective magnetic length after bending corresponds to the straight chord length connecting the two ends, which is calculated as $2 r \sin(\frac{\pi}{6})$. Substituting the radius into this chord formula yields $m \times 2 \times \frac{3l}{\pi} \times \frac{1}{2}$, which directly simplifies to $\frac{3}{\pi} M$.

A current loop placed in a magnetic field experiences a torque defined by the vector cross product $\tau = M \times B$. Equilibrium occurs when this net torque is zero, which happens when the magnetic moment is oriented either parallel or antiparallel to the magnetic field lines. When aligned parallel, the loop is in a state of stable equilibrium where minor displacements create a restoring torque, whereas an antiparallel alignment results in an unstable equilibrium state where any small disturbance causes a complete reversal.

The earth's magnetic field at the geomagnetic poles is directed entirely along the vertical axis, meaning the horizontal component of the magnetic field drops to zero. Since a compass needle restricted to a horizontal plane relies entirely on this horizontal component to experience a directive torque, its absence leaves the needle with no preferred orientation. Consequently, the needle feels no magnetic force aligning it in any particular direction and will remain stationary wherever it is placed.

The potential energy of a magnetic dipole in a uniform magnetic field is determined by the relation $U = -M B \cos{\theta}$, where $\theta$ represents the angle between the dipole and the field. Stable equilibrium corresponds to an alignment where the angle is zero, minimizing the potential energy. Substituting the given magnetic moment of 0.4 J T^{-1} and magnetic field of 0.16 T into the energy equation yields a product of -0.064 J.

Magnetic materials exhibit distinct responses when exposed to an external magnetic field based on their atomic structure and susceptibility. Diamagnetic substances are feebly repelled, paramagnetic substances are feebly attracted, and ferromagnetic substances experience strong attraction, while non-magnetic materials remain entirely unaffected. Matching these fundamental behaviors to the observations reveals that sample A is diamagnetic, sample B is paramagnetic, sample C is ferromagnetic, and sample D is non-magnetic, making the statement regarding sample B being paramagnetic correct.

The time period of oscillation for a bar magnet in a vibration magnetometer is inversely proportional to the square root of the magnetic field, expressed by the equation $T = 2\pi\sqrt{\frac{I}{MB}}$. When a competing magnetic field is introduced in the opposite direction, the new net magnetic field is calculated by subtracting the opposing field from the Earth's horizontal component, giving 24 micro tesla minus 18 micro tesla, which equals 6 micro tesla. Taking the ratio of the two time periods and substituting the initial time period of 2 seconds along with the magnetic field values yields a final time period of 4 seconds.

Electromagnets require materials that can be easily magnetized and demagnetized rapidly without retaining residual magnetism when the external magnetizing field is removed. Soft iron serves as the ideal material for this application because it possesses both low retentivity, meaning it retains very little residual field, and low coercivity, meaning it requires minimal opposing field strength to demagnetize. These combined magnetic properties ensure high operational efficiency and negligible energy loss during cyclic magnetization.

Diamagnetic atoms are characterized by completely filled electronic shells where every electron is paired with another of opposite spin. Because the orbital and spin magnetic moments of each pair are equal and oriented in opposite directions, their individual magnetic fields completely cancel each other out. Consequently, this internal cancellation results in a total net magnetic moment of zero for the atom.

The magnetic force experienced by a charged particle is governed by the relation $\vec{F} = q(\vec{v} \times \vec{B})$, which dictates that a magnetic field can only exert a force on moving charges. Because the charge $Q$ is explicitly stated to be stationary, its velocity is zero. Consequently, the resulting magnetic force acting on the charge must be zero.

Diamagnetic materials develop a weak induced magnetic moment in the direction opposite to an applied external magnetic field due to fundamental atomic responses. Because of this opposing magnetization, they experience a repulsive force in the presence of a magnetic field gradient regardless of which pole of a bar magnet is nearby. Consequently, bringing such a substance close to either the north or south pole will consistently push it away.

The work done in rotating a magnetic dipole in an external magnetic field is determined by the formula $W = MB(\cos \theta_1 - \cos \theta_2)$. Substituting the initial angle of zero degrees and the final angle of sixty degrees into this expression yields $W = MB(1 - \cos 60^\circ)$. Multiplying the given magnetic moment and magnetic field values together with the resulting trigonometric factor gives a total work done of 6 J.

Thermal agitation at and above the Curie temperature disrupts the cooperative alignment of atomic magnetic moments that characterizes ferromagnetism. As a result of this disordering effect, the material loses its spontaneous magnetization and transitions into a paramagnetic state. In this higher temperature regime, individual magnetic moments respond weakly and independently to external magnetic fields.

Ferromagnetic substances rely on strong exchange interactions that keep their atomic magnetic domains aligned below a specific characteristic threshold known as the Curie temperature. Exceeding this critical temperature introduces sufficient thermal energy to completely overcome those cooperative quantum forces and randomize the domain structures. Consequently, the substance sheds its permanent ferromagnetic traits and begins to behave as a simple paramagnetic material.

The magnetic moment of a revolving charge is defined as the product of current and the area enclosed by the loop, given by the formula $\mu = I A$. The equivalent current generated by the moving particle is expressed as charge divided by the time period of revolution, where time is the circular circumference divided by the speed. Substituting this current and the area formula $\pi R^2$ into the magnetic moment equation simplifies the expression to $\frac{qvR}{2}$.