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
Subtopic:  Analogy between Electrostatics & Magnetostatics |
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Level 2: 60%+
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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. \(8.76~\text{s}\)
Subtopic:  Analogy between Electrostatics & Magnetostatics |
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A bar magnet with a magnetic moment of \(0.5~\text{A-m}^2\) is suspended in a uniform magnetic field of \(8 \times 10^{-2}~\text{T}.\) How much work is required to rotate the magnet from its most stable position to its most unstable position?
1. \(16 \times 10^{-2}\) J
2. zero
3. \(8 \times 10^{-2}\) J
4. \(4 \times 10^{-2}\) J
Subtopic:  Analogy between Electrostatics & Magnetostatics |
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Level 2: 60%+
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