Assertion (A): Magnetic force between two charge is generally much smaller than the electric force between them.
Reason (R): Speeds of charges are much smaller than the free-space speed of light.
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
Magnetic force \(F_m = qvB\) and electric force \(F_e = qE\). For moving charges, \(B = \frac{v}{c^2}E\). Thus, \(F_m = \frac{v^2}{c^2}F_e\). Since speeds \(v\) of charges are much smaller than the speed of light \(c\), \(F_m\) is much smaller than \(F_e\). Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): Pole pieces of the magnet used in a moving coil galvanometer are given a concave shape to achieve a radial magnetic field.
Reason (R): A radial magnetic field ensures a better current sensitivity and also makes possible to use a linear scale for current measurement.
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
Concave pole pieces ensure a radial magnetic field in a moving coil galvanometer, keeping \(\vec{B}\) always perpendicular to the coil's area vector. This ensures maximum torque \(\tau = NIAB\) and a linear scale (deflection \(\phi \propto I\)), leading to better current sensitivity. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): Parallel current in wires attracts to each other due to magnetic force.
Reason (R): Two electron beams moving parallel to each other repels to each other due to electric force.
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
Wires with parallel currents attract due to magnetic force, so (A) is true. Two parallel electron beams experience electric repulsion due to like charges, so (R) is true. However, the magnetic force (A) and electric force (R) are distinct phenomena. Thus, (R) does not explain (A).
Assertion (A): Two long parallel conductors carrying currents in the same direction experience a force of attraction.
Reason (R): The magnetic fields produced in the space between two long parallel current carrying conductors (by each of these conductors) are in the same direction.
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
Parallel currents in the same direction attract, so (A) is true. For two parallel currents in the same direction, the magnetic fields in the space between them are in opposite directions (e.g., one into the page, one out of the page by Right Hand Rule). Therefore, (R) is false.
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.