Q4. Assertion: an iron nail is attracted by a bar magnet, but a magnetised needle in a uniform field feels no net force. Reason: a net force on a magnetic dipole needs a non-uniform field. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: the nail sits in the magnet’s non-uniform field and gets an induced moment, so it feels a force as well as a torque (NCERT Example 5.1(b), page 140).
Q5. A closely wound solenoid of 800 turns and cross-section 2.5 × 10−4 m carries 3.0 A. (a) What is its magnetic moment? (b) Free to turn about the vertical in a horizontal field of 0.25 T, what torque acts when its axis is at 30° to the field? (NCERT Exercises 5.3 and 5.4)
(a) It acts like a bar magnet along its axis, with m = NIA = 800 × 3.0 × 2.5 × 10−4 = 0.60 J T−1. (b) τ = mB sin θ = 0.60 × 0.25 × 0.5 = 7.5 × 10−2 N m (NCERT Eq. (5.2), page 139). NCERT’s Exercise 5.4 refers to “the solenoid in Exercise 5.5”; the solenoid is the one in Exercise 5.3.
Q6. A closely wound solenoid of 2000 turns and cross-section 1.6 × 10−4 m carries 4.0 A and can turn in a horizontal plane. A horizontal field of 7.5 × 10−2 T makes 30° with its axis. Find its magnetic moment and the force and torque on it. (NCERT Exercise 5.6)
m = NIA = 2000 × 4.0 × 1.6 × 10−4 = 1.28 J T−1 along the axis. The field is uniform, so the force is zero. Torque τ = mB sin θ = 1.28 × 7.5 × 10−2 × 0.5 = 4.8 × 10−2 N m (NCERT Eq. (5.2), page 139).
Q7. A magnetic needle of moment of inertia 1.2 × 10−6 kg m and magnetic moment 0.08 J T−1 oscillates in a horizontal field of 3.0 × 10−5 T. Find the period of small oscillations.
T = 2π√(I/(mB)) = 2π√(1.2 × 10−6/(2.4 × 10−6)) = 2π√0.5 ≈ 4.4 s (beyond NCERT, from τ = −mBθ for small θ).
Q8. Must every magnetic configuration have a north and a south pole? Think of a toroid. (NCERT Example 5.1(c))
Not necessarily. NCERT: it is true only if the source of the field has a net non-zero magnetic moment, and this is not so for a toroid or even for a straight infinite conductor (NCERT page 140); give that in an exam. An ideal continuously wound toroid has its field confined within it, with no external north and south ends, and a straight infinite wire’s total magnetic dipole moment is not a well-defined finite quantity (reasoned). NCERT’s “only if” is about the configuration as a whole; strictly, zero net dipole moment does not rule out local poles or a field nearby: two opposite dipoles side by side cancel their net moment, but each keeps its own poles and field (reasoned by superposition).
Q9. Two identical-looking iron bars A and B are given, and one of them is definitely magnetised; you do not know which. Using only the bars, how can you tell whether both are magnetised, and if only one is, which? (NCERT Example 5.1(d))
NCERT’s answer: bring different ends of the bars closer. A repulsive force in some situation establishes that both are magnetised; if it is always attractive, then one of them is not magnetised. Since a bar magnet’s field is strongest at the ends and weakest at the centre, lower one end of A first on an end of B and then on the middle of B: if A feels no force at B’s middle, B is the magnet; if nothing changes from B’s end to its middle, A is the magnet (NCERT page 140). Give that in an exam. Strictly, even attraction in every trial does not prove that one bar is unmagnetised: a strong magnet can induce attraction in a weakly magnetised bar, and the field at a real bar’s middle is small rather than exactly zero, so this is a qualitative test (reasoned).