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Q. No.Two identical small bar magnets each of dipole moment \(3 \sqrt{5} ~\text{J/T}\) are placed at a centre to centre separation of \(10~\text{cm},\) with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point \(P\) midway between the magnets is \(\alpha \times 10^{-3} ~\text{T} .\) The value of \(\alpha\)
\(\left(\mu_0=4 \pi \times 10^{-7} ~\text{Tm/A} \right)\)
1. \(10\)
2. \(12\)
3. \(22\)
4. \(30\)
1. \(10\)
2. \(12\)
3. \(22\)
4. \(30\)
Subtopic: Analogy between Electrostatics & Magnetostatics |
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A circular coil of radius \(2~\text{cm}\) and \(125\) turns carries a current of \(1 ~\text{A}.\) The coil is placed in a uniform magnetic field of magnitude \(0.4~\text{T}.\) The axis of the coil makes an angle of \(30^\circ\) with the direction of the magnetic field. The torque acting on the coil is \(\alpha \times 10^{-4} \text { Nm.}\) The value of \(\alpha\) is:
\((\pi=3.14)\)
1. \(123\)
2. \(222\)
3. \(314\)
4. \(400\)
\((\pi=3.14)\)
1. \(123\)
2. \(222\)
3. \(314\)
4. \(400\)
Subtopic: Analogy between Electrostatics & Magnetostatics |
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A current carrying circular loop of radius \(2~\text{cm} \) with unit normal \(\hat{n}=\dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field \(\vec{B}=B_0(3 \hat{i}+2 \hat{k})\). If \(B_0=4 \times 10^{-3}~\text{T}\) and current \(I=100 \sqrt{2} ~\text{A}\), the torque experienced by the loop is: (in \(\text{Wb.A}\)) (\(\pi=3.14\))
1. \(16 \times 10^{-5} \hat{k}\)
2. \(5024 \times 10^{-7} \hat{k}\)
3. \(5024 \times 10^{-7} \hat{i}\)
4. \(5024 \times 10^{-7} \hat{j}\)
1. \(16 \times 10^{-5} \hat{k}\)
2. \(5024 \times 10^{-7} \hat{k}\)
3. \(5024 \times 10^{-7} \hat{i}\)
4. \(5024 \times 10^{-7} \hat{j}\)
Subtopic: Analogy between Electrostatics & Magnetostatics |
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A short bar magnet placed with its axis at \(30^\circ\) with an external field of \(800\) Gauss, experiences a torque of \(0.016\) N.m. The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3}~\text{J} .\) The Value of \(\alpha\) is:
1. \(70\)
2. \(64\)
3. \(80\)
4. \(80\)
1. \(70\)
2. \(64\)
3. \(80\)
4. \(80\)
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
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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A bar magnet with a magnetic moment of \(5~\text{Am}^2\) is initially in a stable equilibrium within a uniform external magnetic field of \(0.4~\text T.\) The work required to slowly rotate the bar magnet into a position of unstable equilibrium is:
1. \(1~\text J\)
2. \(2~\text J\)
3. \(3~\text J\)
4. \(4~\text J\)
1. \(1~\text J\)
2. \(2~\text J\)
3. \(3~\text J\)
4. \(4~\text J\)
Subtopic: Analogy between Electrostatics & Magnetostatics |
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In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} ~\text{A/m}^2\) and moment of inertia \(5 \times 10^{-6} ~\text{kg-m}^2.\) If it performs \(10\) complete oscillations in \(5~\text{seconds}\) then the magnitude of the magnetic field is: \( [ \text{take}~ \pi^2 ~\text{as}~ 9.85 ]\)
1. \(4~\text{mT}\)
2. \(8~\text{mT}\)
3. \(16~\text{mT}\)
4. \(64~\text{mT}\)
1. \(4~\text{mT}\)
2. \(8~\text{mT}\)
3. \(16~\text{mT}\)
4. \(64~\text{mT}\)
Subtopic: Analogy between Electrostatics & Magnetostatics |
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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 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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Q. No.
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