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Q. No.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. \(5\pi^2\)
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.
Choose the correct answer from the options given below:
| 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) |
| 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 \(DC\)
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 \( L\) has a magnetic moment \(M.\) 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. \(M \over 2\)
2. \({2 M}\)
3. \(\)\(\frac{{M}}{\sqrt{3}}\)
4. \(M\)
1. \(M \over 2\)
2. \({2 M}\)
3. \(\)\(\frac{{M}}{\sqrt{3}}\)
4. \(M\)
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
Choose the correct answer from the options given below:
| List-I (Material) | List-II (Example) | ||
| (A) | Diamagnet | (I) | Alnico |
| (B) | Paramagnet | (II) | Copper |
| (C) | Soft ferromagnet | (III) | Aluminium |
| (D) | Hard ferromagnet | (IV) | Gadolinium |
| 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. \(1<\mu_r<1+\varepsilon\)
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. \(4~\text{mT}\)
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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