A rectangular loop with sides \(10~\text{cm},\) carrying a current \(I=12~\text{A},\) is placed in various orientations as shown in the figures. The loop is subjected to a uniform magnetic field of \(0.3~\text{T}\) in the positive \(z\)-direction.

In which orientations is the loop in (i) stable equilibrium and (ii) unstable equilibrium?
| 1. | \(\mathrm{(a)}\) and \(\mathrm{(b)},\) respectively |
| 2. | \(\mathrm{(a)}\) and \(\mathrm{(c)},\) respectively |
| 3. | \(\mathrm{(b)}\) and \(\mathrm{(d)},\) respectively |
| 4. | \(\mathrm{(b)}\) and \(\mathrm{(c)},\) respectively |
A magnetic needle has a magnetic moment of \(6.7\times 10^{-2}~\text{A-m}^2\) and a moment of inertia of \(7.5\times 10^{-6}~\text{kg-m}^2.\) It performs simple harmonic oscillations in a uniform magnetic field of \(0.01~\text{T}.\) How much time will it take to complete \(10\) oscillations?
| 1. | \(6.65~\text{s}\) | 2. | \(8.89~\text{s}\) |
| 3. | \(7.98~\text{s}\) | 4. | \(8.76~\text{s}\) |