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 \(DC\)
Subtopic:  Bar Magnet |
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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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