Consider the following statements:
(A) If magnetic monopoles existed, the magnetic flux through a closed surface would be \(\mu_0\) times the magnetic charge enclosed by it.
(B) A bar magnet does not exert a torque on itself due to its own field.
(C) A system whose net charge is zero has zero magnetic moment.
(D) Two elements of the same current-carrying wire exert no force on each other.
Which of the above statements are incorrect?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (C) and (D) only
Gauss’s law for magnetism says the net flux of \( \mathbf{B} \) through any closed surface is zero, because no magnetic charges (monopoles) are known. A magnet or a current element also feels no force or torque from its own field.
(A) If magnetic monopoles existed, the magnetic flux through a closed surface would be \( \mu_0 \) times the magnetic charge enclosed by it. — Correct statement. The law would then look like Gauss’s law of electrostatics, with \( \mu_0q_m \) on the right side.
(B) A bar magnet does not exert a torque on itself due to its own field. — Correct statement. No element feels a force or torque from the field that it produces itself.
(C) A system whose net charge is zero has zero magnetic moment. — Incorrect statement. The total charge may be zero, but its current loops can still give a net moment. Atoms of a paramagnetic material are neutral, yet they have a magnetic moment.
(D) Two elements of the same current-carrying wire exert no force on each other. — Incorrect statement. One element of a wire does exert a force on another element of the same wire. This force is zero only for a straight wire.
NCERT (2026-27):
Example 5.4 – “If monopoles existed, the right hand side would be equal to the monopole (magnetic charge) qm enclosed by S. [Analogous to Gauss’s law of electrostatics, ∫S B.Δs = μ0qm …”
Example 5.4 – “(c) No. There is no force or torque on an element due to the field produced by that element itself. …”
Example 5.4 – “(d) Yes. The average of the charge in the system may be zero. Yet, the mean of the magnetic moments due to various current loops may not be zero. …”
Example 5.4 – “… But there is a force (or torque) on an element of the same wire. (For the special case of a straight wire, this force is zero.)”