Magnetism And Matter – NEET UG PhysicsPractice Questions & PYQs

Magnetic shielding relies on enclosing sensitive apparatus within a material possessing high magnetic permeability to successfully divert external magnetic flux lines around the protected interior. Soft iron exhibits an exceptional capacity to concentrate magnetic lines of force through its own structural volume rather than allowing them to cross empty space. When an iron enclosure surrounds a delicate device, external magnetic fields preferentially travel through the iron shell instead of penetrating the enclosed region, thereby creating a magnetically isolated space. Alternative enclosure materials like copper or aluminium lack this high permeability and cannot effectively redirect the magnetic flux.

The mechanical work required to rotate a magnetic dipole through an angle in a uniform magnetic field is given by the formula $W = MB(\cos\theta_1 - \cos\theta_2)$. Calculating the work done to rotate the magnet from the stable equilibrium position of zero degrees to ninety degrees gives $W_1 = MB(\cos 0^{\circ} - \cos 90^{\circ})$, which evaluates to $MB$. Similarly, rotating the magnet from zero degrees to sixty degrees results in $W_2 = MB(\cos 0^{\circ} - \cos 60^{\circ})$, yielding half of that value at $\frac{MB}{2}$. Since the problem states that the first work is $n$ times the second, equating $W_1 = n W_2$ reveals that $MB = n \left(\frac{MB}{2}\right)$, making the value of $n$ equal to $2$.

The magnetic moment of a bar magnet is determined by the product of its pole strength and the magnetic length separating the poles, expressed as $M = m \times l$. When a bar magnet is sliced transversely into two equal halves, the pole strength of each newly formed piece remains unchanged, but its length is reduced to half of the original length. Substituting this new length into the magnetic moment formula yields $M' = m \times \frac{l}{2}$, which simplifies to half of the initial magnetic moment. Therefore, each resulting part possesses a magnetic moment equal to $0.5M$.

Interaction forces between a magnetic field and a material sheet arise either from permanent or induced magnetic properties or from electromagnetic induction effects during relative motion. A magnetic sheet experiences a direct attractive or repulsive force from a magnetic pole, requiring an external force to hold it stationary. When a conducting sheet is moved away from the pole, changing magnetic flux induces eddy currents within the material that generate an opposing magnetic force, thus requiring an external force to maintain a uniform velocity.

According to Lenz's law, any induced current will naturally flow in a direction that opposes the magnetic change causing it. As the North pole of the bar magnet moves away from solenoid-1, end B acquires a South polarity to pull it back, resulting in an induced current through the direction AB. Similarly, the approaching South pole of the magnet induces a repelling South pole at end C of solenoid-2 to push it away, which directs the current through the direction DC.

The magnetic moment of a curved magnet is determined by the product of its pole strength and the shortest straight-line distance between its magnetic poles. Letting the original length be $L$ and pole strength be $m$, bending the bar into an arc subtending an angle of $60^{\circ}$ gives a radius of curvature $R = \frac{3L}{\pi}$ and a chord length of $2R\sin(30^{\circ})$. Substituting this geometry yields a new magnetic moment of $m(2)\left(\frac{3L}{\pi}\right)\left(\frac{1}{2}\right)$, which simplifies to $\frac{3M}{\pi}$.

Diamagnetic materials are characterized by a negative magnetic susceptibility and a relative permeability strictly less than unity, causing them to weakly repel external magnetic fields. The relative permeability $\mu_r$ ranges between zero and one ($0 \leq \mu_r < 1$), which directly implies that the absolute permeability $\mu$ is less than the permeability of free space $\mu_0$, while the magnetic susceptibility $\chi = \mu_r - 1$ falls within the interval from $-1$ to $0$. Therefore, the relation describing relative permeability greater than one combined with a positive epsilon is incorrect because those values correspond to paramagnetic behavior.

The time period of oscillation for a magnetic needle suspended in a uniform magnetic field is given by the formula $T = 2\pi \sqrt{\frac{I}{MB}}$. Since the needle completes 10 oscillations in 10 seconds, the time period evaluates to 1 s. Substituting the given values into the formula produces the relation $1 = 2\pi \sqrt{\frac{10^{-6}/\pi^2}{(1.0 \times 10^{-2})B}}$. Squaring both sides eliminates $\pi^2$ and simplifies the expression to $1 = \frac{4 \times 10^{-6}}{10^{-2} \times B}$. Rearranging this equation isolates the magnetic field strength, yielding a final value of 0.4 mT.

The potential energy of a magnetic dipole in a uniform magnetic field is defined by the dot product $U = -\vec{m}\cdot\vec{B}$, which expands to $-mB \cos\theta$ where $\theta$ represents the angle between the magnetic moment and field vectors. Since the magnetic bar is oriented perpendicularly to the magnetic field, the angle is $90^{\circ}$, making the cosine factor zero and the resulting potential energy equal to zero.

The time period of oscillation for a magnetic needle suspended in a uniform magnetic field is given by the formula ($T = 2\pi\sqrt{\frac{I}{MB}}$), where ($I$) represents the moment of inertia, ($M$) is the magnetic moment, and ($B$) is the magnetic field strength. The time period is determined by dividing the total time of 5 seconds by the 20 complete oscillations, resulting in a period of 0.25 seconds.

Substituting these values into the time period relation leads to the equation ($\frac{1}{4} = 2\pi\sqrt{\frac{9.8 \times 10^{-6}}{M \times 0.049}}$). Squaring both sides of this expression transforms it into the relation ($\frac{1}{16} = 4\pi^2 \frac{9.8 \times 10^{-6}}{M \times 0.049}$). Rearranging the terms to isolate the magnetic moment provides the equation ($M = \frac{4\pi^2 \times 9.8 \times 10^{-6} \times 16}{0.049}$). Performing the calculation evaluates the magnetic moment to $12.8\pi^2 \times 10^{-3}$ Am$^2$, which adjusts to $1280\pi^2 \times 10^{-5}$ Am$^2$ and establishes that $x$ is equal to $1280\pi^2$.

Magnetic susceptibility ($\chi$) indicates how a substance responds to an applied magnetic field, categorizing materials by their internal atomic interactions. Diamagnetic substances exhibit a weak repulsion, which translates to a small negative susceptibility represented by $0 > \chi \geq -1$. Conversely, paramagnetic materials show a weak attraction, corresponding to a small positive value of $0 < \chi < \epsilon$, whereas ferromagnetic substances demonstrate powerful attraction with a massive positive susceptibility of $\chi > > 1$. Purely non-magnetic substances have no interaction with the field at all, making their susceptibility exactly $\chi = 0$.

The new magnetic moment of a bent bar magnet depends on the effective straight-line separation between its two free poles rather than its total arc length. When the bar of length $L$ is bent at its midpoint, each arm has a length of $L/2$ and the angle between them is $60^{\circ}$. The effective distance between the two poles forms an isosceles triangle with the arms, meaning the straight-line distance is given by $2\left(\frac{L}{2}\right)\sin(30^{\circ})$, which simplifies to $L/2$ and results in a magnetic moment of $\frac{M}{2}$.

Paramagnetic materials follow Curie's law, which establishes that magnetic susceptibility is inversely proportional to absolute temperature, represented as $\chi \propto \frac{1}{T}$. Plotting susceptibility $\chi$ against the reciprocal of temperature $\frac{1}{T}$ transforms this inverse relationship into a direct proportionality. Consequently, this graphical representation results in a straight line with a constant positive slope.

Magnetic permeability can be determined using the foundational force equation between two parallel current-carrying conductors. By substituting the dimensions of force, length, current, and distance into the rearranged governing expression, the resulting dimensional formula is obtained as $[MLT^{-2}A^{-2}]$. This physical constant characterizes the ability of a specific medium to permit the penetration of magnetic field lines.

The magnetic field at the centre of a long solenoid is given by the formula $B = \mu_0 n I$, where $n$ represents the number of turns per unit length and $I$ is the current. First, convert the turn density into turns per meter by evaluating 100 turns per millimeter, which gives a value of 100,000 turns per meter. Substituting the permeability of free space, the calculated turn density, and the current into the formula yields a magnetic field strength of 12.56 $\times$ 10^-2 T.

The magnetic dipole moment of a current-carrying coil is defined by the formula $M = NIA$, where $N$ represents the number of turns, $I$ is the current, and $A$ is the area of the loop. For both geometrical shapes formed from the wire of total length 12a, the respective number of turns and enclosed areas are substituted into the formula to evaluate the magnetic moment. Evaluating these geometric configurations yields a magnetic dipole moment of $3Ia^2$ in each respective case.

The magnetic permeability of a medium is calculated using the relation $\mu = \mu_r \mu_0$, where the relative permeability $\mu_r$ is obtained by adding one to the magnetic susceptibility $\chi_m$. Adding one to the given susceptibility of 599 gives a relative permeability of 600. Multiplying this relative permeability by the permeability of free space results in a final material permeability of 2.4$\pi$ $\times$ 10^-4 TmA^-1.

The angle of dip on Earth's surface measures the inclination of the total magnetic field vector relative to the horizontal plane. By convention, this angle is positive when the magnetic field points downwards into the northern hemisphere and negative when it points upwards in the southern hemisphere. Therefore, a positive dip angle of 25 degrees places point A in the northern hemisphere, while a negative dip angle of -25 degrees places point B in the southern hemisphere.

When a diamagnetic material moves within an inhomogeneous magnetic field, the work required to displace it against external forces must be supplied by the electrical energy driving the electromagnet. As the rod is pushed upward, gaining gravitational potential energy, an equivalent amount of electrical energy is drawn from the external current source to maintain the magnetic field against the reaction of the repelled diamagnetic substance.

The area of the rectangular coil is calculated as $A = L \times W$, giving $2.1 \times 10^{-2}$ m $\times 1.25 \times 10^{-2}$ m $= 2.625 \times 10^{-4}$ m$^2$. The magnetic dipole moment is given by $M = NIA$, which evaluates to $250 \times 85 \times 10^{-6}$ A $\times 2.625 \times 10^{-4}$ m$^2 = 5.578 \times 10^{-6}$ A m$^2$. The work done in rotating the magnetic dipole by $180^\circ$ is given by $W = MB(\cos \theta_1 - \cos \theta_2)$, and substituting $B = 0.85$ T and the computed moment into $W = 2MB$ yields a total work of $9.1$ $\mu$J.