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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Match List-I with List-II.
List-I
(Material)
List-II
(Susceptibility (\(\chi\)))
\(\mathrm{A.}\) Diamagnetic \(\mathrm{I.}\) \(\chi=0\)
\(\mathrm{B.}\) Ferromagnetic \(\mathrm{II.}\) \(0>\chi\geq-1\)
\(\mathrm{C.}\) Paramagnetic \(\mathrm{III.}\) \(\chi\gg1\)
\(\mathrm{D.}\) Non-magnetic \(\mathrm{IV.}\) \(0<\chi<\varepsilon\) (a small positive number)
Choose the correct answer from the options given below:
1. \(\text{A-II, B-I, C-III, D-IV}\)
2. \(\text{A-III, B-II, C-I, D-IV}\)
3. \(\text{A-IV, B-III, C-II, D-I}\)
4. \(\text{A-II, B-III, C-IV, D-I}\)
Subtopic:  Magnetic Materials |
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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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Match List-I with List-II 
List-I (Material) List-II (Example)
(A) Diamagnet (I) Alnico
(B) Paramagnet (II) Copper
(C) Soft ferromagnet (III) Aluminium
(D) Hard ferromagnet (IV) Gadolinium
 
Choose the correct answer from the options given below:
1. A-I, B-II, C-III, D-IV
2. A-IV, B-III, C-II, D-I
3. A-III, B-II, C-I, D-IV
4. A-II, B-III, C-IV, D-I
Subtopic:  Magnetic Materials |
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The best suited curve showing the variations of susceptibility (\(\chi\)) of a paramagnetic material in free space with temperature (\(T\)) is: 
1.
 
2.
3.
4.
Subtopic:  Magnetic Materials |
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The magnetic potential energy when a magnetic bar with a magnetic moment \(\vec{M}\) is placed perpendicular to the magnetic field \(\vec{B}\) is:
1. \(\dfrac{-mB}{2}\) 2. zero
3. \(-mB\) 4. \(mB\)
Subtopic:  Analogy between Electrostatics & Magnetostatics |
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The incorrect relation for a diamagnetic material (all the symbols carry their usual meaning and \(\varepsilon\) is a small positive number) is:
1. \(\mu<\mu_{0}\) 2. \(0\leqslant\mu_{\mathrm{r}}<1\)
3. \(-1\leqslant\chi<0\) 4. \(1<\mu_r<1+\varepsilon\)
Subtopic:  Magnetic Materials |
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The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, \(1.0\times10^{-2}~\text{A m}^{2}\text{and}~\frac{10^{-6}}{\pi^{2}}~\text{kg m}^{2}.\) If it completes \(10\) oscillations in \(10~\text s,\) the magnitude of the magnetic field is:
 
1. \(0.4~\text T\)
2. \(4~\text T\)
3. \(0.4~\text{mT}\)
4. \(4~\text{mT}\)
Subtopic:  Magnetization & Magnetic Intensity |
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