Identify the correct statements regarding the magnetic field and magnetic force:
(A) The magnetic field due to a number of sources is the vector addition of the magnetic field of each individual source.
(B) If the velocity of a charged particle moving in a uniform magnetic field is parallel or antiparallel to its direction, the force acting on the charged particle is zero.
(C) The magnetic force is zero if a charge is moving perpendicular to the direction of the magnetic field.
(D) The direction of the magnetic force acting on a charged particle moving in a uniform magnetic field depends on the nature of its charge.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (D) only
The magnetic force on a moving charge is \( \vec{F} = q(\vec{v}\times\vec{B}) \), of magnitude \( qvB\sin\theta \), and magnetic fields obey the principle of superposition.
(A) The magnetic field due to a number of sources is the vector addition of the magnetic field of each individual source. — Correct. This is the superposition principle for magnetic fields.
(B) If the velocity of a charged particle moving in a uniform magnetic field is parallel or antiparallel to its direction, the force acting on the charged particle is zero. — Correct. For \( \theta = 0^\circ \) or \( 180^\circ \), \( \sin\theta = 0 \), so \( F = 0 \).
(C) The magnetic force is zero if a charge is moving perpendicular to the direction of the magnetic field. — Incorrect. For \( \theta = 90^\circ \), \( \sin\theta = 1 \), so the force is maximum, \( F = qvB \).
(D) The direction of the magnetic force acting on a charged particle moving in a uniform magnetic field depends on the nature of its charge. — Correct. Reversing the sign of q reverses \( q(\vec{v}\times\vec{B}) \), so positive and negative charges are deflected in opposite directions.
NCERT (2026-27):
Sources and Fields – “… Experimentally, it is found to obey the principle of superposition: the magnetic field of several sources is the vector addition of magnetic field of each individual source.”
Magnetic Field, Lorentz Force – “… (i) It depends on q, v and B (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.”
Magnetic Field, Lorentz Force – “… The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.”