Assertion (A): Force on a current carrying wire of length \(dvec{l}\) placed in magnetic field \(vec{B}\) is given by \(d\vec{F} = Id\vec{l} \times \vec{B}\).
Reason (R): Net force on a current carrying loop in a non-uniform magnetic field must be non-zero.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The Lorentz force law states \(d\vec{F} = I(d\vec{l} \times \vec{B})\), so (A) is true. For a loop in a uniform field, net force is zero; in a non-uniform field, it is generally non-zero, so (R) is true. However, (R) is a consequence of the force law, not an explanation of the force law itself.
Assertion (A): The nature of electromagnetic force acting on a moving charged particle in external magnetic field is frame dependent.
Reason (R): The force acting on a charged particle always varies with shift of frame.
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 false because the total electromagnetic force is invariant under Lorentz transformations, meaning its nature is not frame dependent. Reason (R) is also false; while the magnetic force itself varies with frame, the total electromagnetic force remains invariant. Therefore, both assertion and reason are false.
Assertion (A): When a straight wire carrying current is placed along the axis of a current carrying ring, it starts rotating about the wire.
Reason (R): Charged ring will experience a torque when current carrying cable will pass through its axis.
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 false. A straight wire carrying current along the axis of a ring produces a magnetic field that is perpendicular to the current elements of the ring. Consequently, the magnetic force \(I(\vec{dl} \times \vec{B}))\ on each element is zero, resulting in no net force or torque on the ring.
Reason (R) is also false because no torque is experienced under these conditions. Both assertion and reason are false.
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
View Answer
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
View Answer
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
View Answer
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
View Answer
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): 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
View Answer
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).