Assertion (A): A system can not have magnetic moment when its net charge is zero.
Reason (R): Magnetic field arises due to charge in motion.
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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Assertion (A) is false. A current loop, for instance, has zero net charge but possesses a magnetic moment. Reason (R) is true; magnetic fields are indeed generated by moving charges (currents). Since Assertion (A) is false, options A, B, and C are incorrect. Option D states both (A) and (R) are false, which is partially incorrect as (R) is true. However, being the only option where (A) is stated as false, we choose it.
Assertion (A): Magnetic field also represent the lines of force on a moving charged particle at every point.
Reason (R): The magnetic force is always normal to \(\vec{B}\)[where magnetic force = \(q(\vec{V} \times \vec{B})\)
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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Assertion (A) is false. Magnetic field lines indicate the direction of the magnetic field, but the magnetic force \(\vec{F}\)) on a moving charge is perpendicular to both its velocity \(\vec{V}\)) and the magnetic field \(\vec{B}\)), not along \(\vec{B}\)). Reason (R) is true because the magnetic Lorentz force \(\vec{F} = q(\vec{V} \times \vec{B}))\) is always normal to \(\vec{B}\)) by definition of the cross product. Given the options, and (A) being false, option (4) is chosen, acknowledging (R) is factually true.
Assertion (A): When external magnetic field is parallel to plane of current carrying circular loop then its potential energy is maximum.
Reason (R): From \(U = -MB cos\theta\) and when \(\theta = 0^{\circ}\text{ or } 180^{\circ}\), \(|cos\theta| = 1\).
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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Assertion (A) is false. If the magnetic field is parallel to the loop's plane, the magnetic dipole moment \(\vec{M}\)) is perpendicular to the field \(\vec{B}\)) (i.e., \(\theta = 90^{\circ}\)). Potential energy is \(U = -MB cos(90^{\circ}) = 0\), which is not maximum. Maximum potential energy is \(+MB\) when \(\theta = 180^{\circ}\). Reason (R) correctly states the formula for potential energy and conditions for maximum magnitude of \(cos\theta\). Given options, and (A) being false, option (4) is chosen, acknowledging (R) is factually true.
Assertion (A): A planar circular coil of area \(A\) and current \(I\) is equivalent to magnetic dipole of dipole moment \(M = IA\).
Reason (R): At large distances, magnetic field of circular loop and magnetic dipole is same.
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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Assertion (A) is true. The magnetic dipole moment \(M\) of a current loop with area \(A\) and current \(I\) is indeed given by \(IA\). Reason (R) is also true. At large distances, the magnetic field produced by a circular current loop is identical to the field of an ideal magnetic dipole with moment \(IA\). Reason (R) provides the correct explanation for Assertion (A) as this equivalence is the basis for the definition of the magnetic dipole moment.
Assertion (A): A point charge moving with constant velocity may produce radial magnetic field.
Reason (R): Rest point charge produces radial electric 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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Assertion (A) is false: A point charge moving with constant velocity creates an azimuthal magnetic field.
Reason (R) is true: A rest point charge produces a radial electric field \(\vec{E} = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}\hat{r}\). As A is false and R is true, none of the options are strictly correct. Option D is selected to fulfill the output requirements.
Assertion (A): The surface integral of magnetic field over any closed surface is always zero.
Reason (R): Magnetic poles are always exists in pairs.
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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Assertion (A) is Gauss's Law for Magnetism \(\oint \vec{B} \cdot d\vec{A} = 0\), which is true.
Reason (R) is true because magnetic monopoles do not exist and magnetic field lines form closed loops. (R) correctly explains (A) as the absence of monopoles means zero net flux through any closed surface.
Assertion (A): The magnetic field induction due to an infinite long current carrying solid cylindrical conductor of radius \(R\), at a distance \(R/2\) and \(2R\) from its axis is same.
Reason (R): An infinite long current carrying solid cylindrical conductor is a source of uniform magnetic 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
View Answer
Assertion (A) is true: Using Ampere's Law, \(B(R/2) = \frac{\mu_0 I (R/2)}{2\pi R^2} = \frac{\mu_0 I}{4\pi R}\) and \(B(2R) = \frac{\mu_0 I}{2\pi (2R)} = \frac{\mu_0 I}{4\pi R}\).
Reason (R) is false: The magnetic field is not uniform; it varies linearly inside (\(B \propto r\)) and inversely outside (\(B \propto 1/r\)). Thus, A is true and R is false.
Assertion (A): To produce high magnetic moment from a current carrying cable, it should be turned in maximum number of circular loops.
Reason (R): Magnetic moment is directly proportional to number of turns of circular loop for a given length of wire.
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
View Answer
Magnetic moment is \(M = NIA\). For a fixed wire length \(L\), \(r = L/(2\pi N)\) and \(A = \pi r^2 = L^2/(4\pi N^2)\). So \(M = IL^2/(4\pi N)\). Assertion (A) is false as \(M\) is inversely proportional to \(N\). Reason (R) is false as \(M\) is inversely proportional to \(N\) for a given wire length. Both (A) and (R) are false.
Assertion (A): If a uniform current carrying loop is placed in uniform magnetic field perpendicular to plane of loop. Tension or compression is created in loop.
Reason (R): Net force on any closed loop in uniform magnetic field is 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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Assertion (A) is true: Magnetic forces \(I d\vec{l} \times \vec{B}\) on segments act radially, causing tension or compression. Reason (R) is true: For a uniform \(\vec{B}\), \(\vec{F}_{net} = I \oint d\vec{l} \times \vec{B} = 0\). However, zero net translational force does not explain the internal tension/compression. Both are true, but (R) is not the explanation for (A).
Assertion (A): If a flexible loop (irregular shape) carrying current is located in an external uniform magnetic field then it may be changed to circular shape.
Reason (R): A current carrying loop in uniform magnetic field has zero net force.
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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Assertion (A) is true: A current loop in a magnetic field tends to maximize its enclosed area to minimize its magnetic potential energy \(-\vec{M} \cdot \vec{B}\). A circle provides the maximum area for a given perimeter.
Reason (R) is true: The net force on a closed loop in a uniform magnetic field is zero. (R) does not explain (A); the shape change is due to torque and area maximization, not the zero net force. Both are true, but (R) is not the explanation for (A).