In a uniform magnetic field of \(0.049~\text T\), a magnetic needle performs \(20\) complete oscillations in \(5\) seconds as shown. The moment of inertia of the needle is \(9.8 × 10^{-6} ~\text{kg m}^2\). If the magnitude of magnetic moment of the needle is \(x \times 10^{-5 }~\text {Am}^2;\) then the value of '\(x\)' is:
                
1. \(128\pi^2\)
2.  \(50\pi^2\)
3. \(1280\pi^2\)
4. \(5\pi^2\)
Subtopic:  Bar Magnet |
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In the above diagram, a strong bar magnet is moving towards solenoid-\(2\) from solenoid-\(1\). The direction of induced current in solenoid-\(1\) and that in solenoid-\(2\), respectively, are through the directions:
                        
1. \(BA\) and \(CD\)
2. \(AB\) and \(CD\)
3. \(BA\) and \(DC\)
4. \(AB\) and \(DC\)
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An iron bar of length \(\mathrm L\) has magnetic moment \(\mathrm M.\) It is bent at the middle of its length such that the two arms make an angle \(60^\circ\) with each other. The magnetic moment of this new magnet is:
1. \( \mathrm M \over 2\)
2. \( \mathrm {2 M}\)
3. \(\)\(\frac{\mathrm{M}}{\sqrt{3}}\)
4. \(\mathrm M\)
Subtopic:  Bar Magnet |
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The length of a magnetized iron bar is \(L\) and its magnetic moment is \(M.\) When this bar is bent to form a semicircle its magnetic moment is:
1. \(M\) 2. \(\dfrac{M\pi}{2}\)
3. \( \dfrac{M}{2\pi}\) 4. \(\dfrac{2M}{\pi}\)
Subtopic:  Bar Magnet |
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The magnetic moment of an iron bar is \(M.\) It is now bent in such a way that it forms an arc section of a circle subtending an angle of \(60^\circ\) at the center. The magnetic moment of this arc section is:
1. \(\frac{3 M}{\pi}\)
2. \(\frac{4M}{\pi}\)
3. \(\frac{ M}{\pi}\)
4. \(\frac{2 M}{\pi}\)
Subtopic:  Bar Magnet |
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The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole. Which configuration has the highest net magnetic dipole moment?

1. 2.
3. 4.
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A bar magnet of length \(l\) and magnetic dipole moment \(M\) is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be:

1. \(\dfrac{3M}{\pi}\) 2. \(\dfrac{2M}{l\pi}\)
3. \(\dfrac{M}{ 2}\) 4. \(M\)
Subtopic:  Bar Magnet |
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A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 s in the earth's horizontal magnetic field of 24 μT. When a horizontal field of 18 μT is produced opposite to the earth's field by placing a current-carrying wire, the new time period of the magnet will be:

1. 1 s

2. 2 s

3. 3 s

4. 4 s

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Two identical bar magnets are fixed with their centres at a distance d apart. A stationary charge Q is placed at P in between the gap of the two magnets at a distance D from the centre O as shown in the figure:

The force on the charge Q is in:
1. direction along OP
2. direction along PQ
3. direction perpendicular to the plane of paper
4. zero

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A bar magnet having a magnetic moment of \(2\times10^4\) JT-1 is free to rotate in a horizontal plane. A horizontal magnetic field \(B=6\times10^{-4}\) T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction \(60^\circ\) from the field is:
1. \(0.6\) J
2. \(12\) J
3. \(6\) J
4. \(2\) J
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