Q. No.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 |
1. \(3\pi~\text{Am}^{-1}\)
2. \(30000\pi~\text{Am}^{-1}\)
3. \(300~\text{Am}^{-1}\)
4. \(30000~\text{Am}^{-1}\)
A magnetic needle of magnetic moment \(6.7\times 10^{-2}~\text{A m}^2\) and moment of inertia \(7.5\times 10^{-6}~\text{kg m}^2\) is performing simple harmonic oscillation in a magnetic field of \(0.01~\text{T}.\) Time taken for \(10\) complete oscillations is:
1. \(6.65~\text{s}\)
2. \(8.89~\text{s}\)
3. \(6.98~\text{s}\)
4. \(8.76~\text{s}\)
1. \(2~\text{mA}\)
2. \(20~\mu\text{A}\)
3. \(1~\text{mA}\)
4. \(40~\mu\text{A}\)
Two magnetic dipoles, \(X\) and \(Y,\) are separated by a distance \(d,\) with their axes oriented perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X.\) A charged particle with charge \(q\) moves with velocity \(v\) through their midpoint \(P,\) which makes an angle \(\theta=45^\circ\) with the horizontal axis, as shown in the diagram. Assuming \(d\) is much larger than the dimensions of the dipoles, the magnitude of the force acting on the charged particle at this instant is:
| 1. | \( 0 \) | 2. | \(\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{M}{\left(\dfrac{d}{2}\right)^3} \times q v \) |
| 3. | \(\sqrt{2}\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{M}{\left(\dfrac{d}{2}\right)^3} \times q v \) | 4. | \(\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{2 M}{\left(\dfrac{d}{2}\right)^3} \times q v\) |
1. \(285~\text{A/m}\)
2. \(2600~\text{A/m}\)
3. \(520~\text{A/m}\)
4. \(1200~\text{A/m}\)
Magnetic materials used for making permanent magnets (\(\text{P}\)) and magnets in a transformer (\(\text{T}\)) have different properties of the following, which property best matches for the type of magnet required?
| 1. | \(\text{T}\) : Large retentivity, small coercivity |
| 2. | \(\text{P}\) : Small retentivity, large coercivity |
| 3. | \(\text{T}\) : Large retentivity, large coercivity |
| 4. | \(\text{P}\) : Large retentivity, large coercivity |
A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field \(\vec{B}\). Then the field inside the paramagnetic substance is:
| 1. | Zero |
| 2. | \(\vec{B}\) |
| 3. | much larger than \(|\vec{B}|\) and parallel to \(\vec{B}\) |
| 4. | much larger than \(|\vec{B}|\) and opposite to \(\vec{B}\) |
A small bar magnet placed with its axis at \(30^\circ\) with an external field of \(0.06\) T experiences a torque of \(0.018\) Nm. the minimum work required to rotate it from its stable to unstable equilibrium position is:
1. \(7.2\times 10^{-2}~\text{J}\)
2. \(11.7\times 10^{-3}~\text{J}\)
3. \(9.2\times 10^{-3}~\text{J}\)
4. \(6.4\times 10^{-2}~\text{J}\)
A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:
| 1. | increase in size but no change in orientation |
| 2. | have no relation with an external magnetic field |
| 3. | decrease in size and change its orientation |
| 4. | may increase or decrease in size and change its orientation |
© 2025 GoodEd Technologies Pvt. Ltd.