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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. \(\left(\dfrac{\mu_0}{4 \pi}\right) \dfrac{2 M}{\left(\dfrac{d}{2}\right)^3} \times q v\)
Subtopic:  Bar Magnet |
Level 3: 35%-60%
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A bar magnet is demagnetised by placing it inside a solenoid of length \(0.2~\text{m},\) having \(100\) turns, and carrying a current of \(5.2~\text{A}.\) What is the coercivity of the bar magnet?
1. \(285~\text{A/m}\) 2. \(2600~\text{A/m}\)
3. \(520~\text{A/m}\) 4. \(1200~\text{A/m}\)
Subtopic:  Bar Magnet |
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Level 2: 60%+
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A small bar magnet is placed in a uniform external magnetic field of magnitude \(0.06\text{ T},\) such that its magnetic axis makes an angle of \(30^\circ\) with the field. If the magnet experiences a torque of \(0.018\text{ N-m},\) what is the minimum work required to rotate the magnet from its stable equilibrium position to its unstable equilibrium position?
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. \(6.4\times 10^{-2}~\text{J}\)

Subtopic:  Bar Magnet |
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A bar magnet having a magnetic moment of \(2.0\times10^{5}~\text{JT}^{-1}\) is placed along the direction of the uniform magnetic field of magnitude, \(B=14\times10^{-5}~\text{T}\). The work done in rotating the magnet slowly through \(60^\circ \) from the direction of the field is:
1. \(14~\text{J}\)
2. \(8.4~\text{J}\)
3. \(4~\text{J}\)
4. \(1.4~\text{J}\)
Subtopic:  Bar Magnet |
 91%
Level 1: 80%+
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Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be :
1. 2 : 1
2. 8 : 3
3. 1 : 3
4. 27 : 16
Subtopic:  Bar Magnet |
 83%
Level 1: 80%+
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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. \(4~\text J\) 
Subtopic:  Bar Magnet |
 64%
Level 2: 60%+
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A dipole having moment \(M\) is placed in two magnetic fields of strength \(B_1\) and \(B_2\) respectively. If the dipole oscillates \(60\) time in \(20\) s in \(B_1\)  and \(60\) oscillations in \(30\) s in \(B_2\) . Then \(\frac{B_1}{B_2}=\)
1. \(3 \over 2\) 2. \(2 \over 3\)
3. \(4 \over 9\) 4. \(9 \over 4\)
Subtopic:  Bar Magnet |
 70%
Level 2: 60%+
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A conducting bar of length \({L}\) is free to slide on two parallel conducting rails as shown in the figure. Two resistors \({R}_1\) and \({R}_2\) are connected across the ends of the rails. There is a uniform magnetic field \(\vec B\) pointing into the page. An external agent pulls the bar to the left at a constant speed \({v}.\) The correct statement about the directions of induced currents \({I}_1\) and \({I}_2\) flowing through \({R}_1\) and \({R}_2\) respectively is:
  
1. \({I}_1\) is in an anticlockwise direction and \(\text{I}_2\) is in a clockwise direction
2. Both \({I}_1\) and \({I}_2\) are in an anticlockwise direction
3. Both \({I}_1\) and \({I}_2\) are in a clockwise direction
4. \({I}_1\) is in a clockwise direction and \({I}_2\) is in an anticlockwise direction

 
Subtopic:  Bar Magnet |
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A straight magnetic strip has a magnetic moment of \(44~\text{Am}^2.\) If the strip is bent in a semi-circular shape, its magnetic moment will be:
(given \(\pi=\frac{22}{7}\))
1. \(28~\text{Am}^2.\)
2. \(34~\text{Am}^2.\)
3. \(46~\text{Am}^2.\)
4. \(12~\text{Am}^2.\)
Subtopic:  Bar Magnet |
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A bar magnet has total length \(2l=20 \) units and the field point \(P\) is at a distance \(d=10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is \(1\%,\) then uncertainty of the magnetic field at point \(P\) is:

1. \(5\%\)
2. \(3\%\)
3. \(4\%\)
4. \(10\%\)
Subtopic:  Bar Magnet |
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