Assertion (A): A charged particle enters a uniform magnetic field with a velocity inclined to the field direction at \( 60^\circ \). The particle will move along a circular path inside the magnetic field.
Reason (R): Magnetic force on a charge inside a magnetic field provides centripetal force for the circular motion of the charge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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When a charged particle's velocity is inclined to a uniform magnetic field, the component of velocity perpendicular to the field leads to circular motion, while the parallel component leads to linear motion. The combination results in a helical path, which includes a circular component. Thus, (A) is true. The magnetic force \( \vec{F} = q(\vec{v} \times \vec{B}) \) is always perpendicular to \( \vec{v} \), providing the centripetal force \( F_c = qv_{\perp}B \) for the circular motion. So (R) is true and explains the circular aspect of (A).
Assertion (A): A current-carrying coil placed in a uniform magnetic field experiences a force which depends on the orientation of plane of the coil relative to the field direction.
Reason (R): A current-carrying conductor placed in a magnetic field experiences a force \( F = I L B sin \theta \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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A current-carrying coil in a uniform magnetic field experiences a torque \( \tau = NIAB sin \alpha \), where \( \alpha \) is the angle between the area vector and the magnetic field. This torque and the resultant forces clearly depend on the coil's orientation, making (A) true. The force on a segment of a current-carrying conductor is given by \( F = ILB sin \theta \). This fundamental principle explains the origin of the forces acting on the sides of the coil, leading to the overall torque and forces in (A). Both (A) and (R) are true, and (R) is the correct explanation of (A).
Assertion (A): A charged particle moving in a magnetic field in general, experiences a force but its kinetic energy remains constant.
Reason (R): Work done by magnetic force is always zero.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Magnetic force \( \vec{F} = q(\vec{v} \times \vec{B}) \) is always perpendicular to velocity \( \vec{v} \). Thus, work done \( W = \vec{F} \cdot d\vec{r} = 0 \). By the Work-Energy Theorem, if work done is zero, the kinetic energy remains constant. Both assertion (A) and reason (R) are true, and (R) correctly explains (A).
Assertion (A): Electric force between two like charged particles is repulsive but magnetic force between them could be attractive or repulsive or absent depending on the features of their motion.
Reason (R): Magnetic field does not interact with static charges.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Electric force between like charges is indeed repulsive. Magnetic force between moving charges can be attractive (parallel motion), repulsive (anti-parallel motion), or absent, depending on their relative velocities. Magnetic fields only interact with moving charges, not static ones. Both assertion (A) and reason (R) are true. However, (R) explains why magnetic force requires motion, not the diverse nature (attractive/repulsive) of the force itself.
Assertion (A): Magnetic field arises due to charge in motion but a system may have magnetic moment even though its net charge is zero.
Reason (R): Uncharged magnetic material may have dipole moment.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Magnetic fields are produced by moving charges. Atoms/molecules with electron motion have magnetic moments even if neutral. Uncharged materials like ferromagnets have atomic dipole moments. Reason (R) explains how uncharged materials can have dipole moments, thus supporting Assertion (A).
Assertion (A): Permeability of a ferromagnetic material is independent of the applied magnetic field.
Reason (R): Permeability of ferromagnetic substances is lower for higher value of applied field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Permeability \(\mu\) of ferromagnetic materials is highly dependent on the applied field and exhibits hysteresis, making Assertion (A) false. While permeability decreases at very high fields due to saturation, it initially increases. So, Reason (R) is not universally true. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): A system displaying a hysteresis loop, such as a ferromagnet is a device for storing memory.
Reason (R): A ferromagnetic substance remains magnetised even after external field is removed.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Hysteresis means a material retains magnetization (retentivity) when the external field is removed. This residual magnetism allows the material to 'remember' its magnetic state, forming the basis of magnetic memory. Thus, Reason (R) correctly explains Assertion (A).
Assertion (A): The product of magnetic susceptibility and absolute temperature of a paramagnetic substance is a constant.
Reason (R): Paramagnetic substances obey Curie’s law.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Curie's law states that for paramagnetic substances, magnetic susceptibility (chi) is inversely proportional to absolute temperature (T), i.e., (chi = C/T). This implies (chi T = C), a constant. So Reason (R) directly explains Assertion (A).
Assertion (A): The permanent magnetic moment of the atoms of a material is zero. The material must be diamagnetic.
Reason (R): Hard magnetic materials have high retentivity, high coercivity and large hysteresis- loss and are suitable for permanent magnetism.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Diamagnetic materials are characterized by the absence of permanent atomic magnetic moments, making Assertion (A) true. Hard magnetic materials need high retentivity and coercivity for permanent magnetism, making Reason (R) true. However, the two statements describe different properties and are not causally related.
Assertion (A): The poles of magnet cannot be separated by breaking into two pieces.
Reason (R): The magnetic moment will be reduced to half when a magnet is broken into two equal pieces.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Magnetic monopoles do not exist; breaking a magnet creates two smaller magnets, each with North and South poles, making Assertion (A) true. Breaking a uniform magnet into two equal pieces reduces its magnetic moment (M = ml) by half (as length (l) is halved), making Reason (R) true. Reason (R) describes a quantitative change, not the fundamental reason for non-separation of poles.