Q4. Assertion: a current loop in a uniform magnetic field can be in equilibrium with its magnetic moment pointing against the field. Reason: the torque m × B is zero when m and B are antiparallel. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion; but the equilibrium is unstable, since any small rotation produces a torque that turns the loop further (NCERT page 126).
Q5. A current-carrying circular loop lies on a smooth horizontal table. Can a uniform magnetic field make it spin about the vertical axis? (NCERT Example 4.11(a))
No. That would need a vertical torque, but τ = IA × B with A vertical always lies in the horizontal plane of the loop, whatever B is (NCERT page 128).
Q6. How much work is needed to turn a coil of magnetic moment 10 A m from alignment with a 2.0 T field to the opposite direction?
W = mB(cos 0° − cos 180°) = 2mB = 2 × 10 × 2.0 = 40 J (reasoned from U = −m·B, NCERT Chapter 5, Eq. (5.3), page 139).
Q7. A wire of length L is bent into a circular coil of one turn and carries a current I. If the same wire is bent into a coil of two turns, how does its magnetic moment change?
One turn: R = L/(2π) and m = IπR = IL/(4π). Two turns: R = L/(4π), so m = 2IπR = 2IπL/(16π) = IL/(8π). The moment halves (reasoned from NCERT Eq. (4.24), page 126).
Q8. An electron goes round a circle of radius 5.3 × 10−11 m at 2.2 × 106 m/s. Find the current it is equivalent to and its magnetic moment.
Turns per second: v/(2πr) ≈ 6.6 × 1015. Current: I = e × 6.6 × 1015 ≈ 1.1 × 10−3 A. Moment: m = IπR = evr/2 ≈ 9.3 × 10−24 A m. It points opposite to the orbital angular momentum, because the electron is negative (reasoned from NCERT Eq. (4.22)).