- 1(current)
Q. No.A circular current loop of radius \(R\) is placed inside square loop of side length \(L(L>>R)\) such that they are co-planar and their centres coincide. The permeability of free space is \(\mu_0.\) The mutual inductance between circular loop and square loop is:
1. \(2 \sqrt{2} \dfrac{\mu_0 L^2}{R} \)
2. \(\sqrt{2} \dfrac{\mu_0 L^2}{R} \)
3. \( \sqrt{2} \dfrac{\mu_0 R^2}{L} \)
4. \(2 \sqrt{2} \dfrac{\mu_0 R^2}{L}\)
1. \(2 \sqrt{2} \dfrac{\mu_0 L^2}{R} \)
2. \(\sqrt{2} \dfrac{\mu_0 L^2}{R} \)
3. \( \sqrt{2} \dfrac{\mu_0 R^2}{L} \)
4. \(2 \sqrt{2} \dfrac{\mu_0 R^2}{L}\)
Subtopic: Mutual Inductance |
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Consider \({I}_1\) and \({I}_2\) are the currents flowing simultaneously in two nearby coils \(1\) & \(2\), respectively. If \(L_1=\) self-inductance of coil \(1\), \(M_{12} =\) mutual inductance of coil \(1\) with respect to coil \(2,\) then the value of induced emf in coil \(1\) will be:
1. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_1}{{dt}}-{M}_{12} \dfrac{{dI}_1}{{dt}} \)
2. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_1}{{dt}}-{M}_{12} \dfrac{{dI}_2}{{dt}} \)
3. \(\varepsilon_1=-L_1 \dfrac{{dI}_2}{{dt}}+{M}_{12} \dfrac{{dI}_2}{{dt}} \)
4. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_2}{{dt}}-{M}_{12} \dfrac{{dI}_1}{{dt}} \)
1. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_1}{{dt}}-{M}_{12} \dfrac{{dI}_1}{{dt}} \)
2. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_1}{{dt}}-{M}_{12} \dfrac{{dI}_2}{{dt}} \)
3. \(\varepsilon_1=-L_1 \dfrac{{dI}_2}{{dt}}+{M}_{12} \dfrac{{dI}_2}{{dt}} \)
4. \(\varepsilon_1=-{L}_1 \dfrac{{dI}_2}{{dt}}-{M}_{12} \dfrac{{dI}_1}{{dt}} \)
Subtopic: Mutual Inductance |
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Two concentric conducting coplanar rings of radius \(a\) and \(b\) are placed as shown in the diagram \((a<<b) .\) Then the coefficient of mutual inductance of rings is:
1. \(\dfrac{\mu_0 \pi b^2}{a}\)
2. \(\dfrac{\mu_0 \pi a^2}{2 b}\)
3. \(\dfrac{\mu_0 a^2}{2 b}\)
4. \(\dfrac{\mu_0 a^3}{2 \pi b^2}\)
1. \(\dfrac{\mu_0 \pi b^2}{a}\)
2. \(\dfrac{\mu_0 \pi a^2}{2 b}\)
3. \(\dfrac{\mu_0 a^2}{2 b}\)
4. \(\dfrac{\mu_0 a^3}{2 \pi b^2}\)
Subtopic: Mutual Inductance |
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A small circular loop of radius \(r\) is placed in the plane of a square loop of side length \(L\) \((r \ll L).\) A circular loop is at the center of the square as shown in the figure. The mutual inductance of the given system is:
| 1. | \({\dfrac{\mu_{0}r^{2}}{\sqrt{2}L}}\) | 2. | \({\dfrac{\pi\mu_{0}r^{2}}{2L}}\) |
| 3. | \({\dfrac{2\sqrt{2}\mu_{0}r^{2}}{L}}\) | 4. | \({\dfrac{4\mu_{0}r^{2}}{L}}\) |
Subtopic: Mutual Inductance |
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A small square loop of wire of side \(\ell \) is placed inside a large square loop of wire \(L\) \((L\gg l).\) Both loops are coplanar and their centres coincide at point \(O\) as shown in the figure. The mutual inductance of the system is:
| 1. | \(\dfrac{2\sqrt{2}\mu _{0}L^{2}}{\pi \ell}\) | 2. | \(\dfrac{\mu_{0} \ell^{2}}{2 \sqrt{2} \pi {L}} \) |
| 3. | \(\dfrac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi {L}} \) | 4. | \(\dfrac{\mu_{0} L^{2}}{2 \sqrt{2} \pi \ell}\) |
Subtopic: Mutual Inductance |
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A small square loop of side \(a\) and one turn is placed concentrically and coplanarly inside a larger square loop of side \(b\) and one turn, where \(b\gg a.\) A steady current \(I\) flows through the larger loop. Assuming that the magnetic field produced by the larger loop is approximately uniform over the area of the smaller loop, the mutual inductance between the two loops is:
| 1. | \(\dfrac{\mu_0}{4 \pi} \dfrac{8 \sqrt{2}}{b}\) | 2. | \(\dfrac{\mu_0}{4 \pi} 8 \sqrt{2} \dfrac{b^2}{a}\) |
| 3. | \(\dfrac{\mu_0}{4 \pi} \dfrac{8 \sqrt{2}}{{a}}\) | 4. | \(\dfrac{\mu_0}{4 \pi} 8 \sqrt{2} \dfrac{a^2}{b}\) |
Subtopic: Mutual Inductance |
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Two coil '\(P\)' and '\(Q\)' are separated by some distance. When a current of \(3~\text{A}\) flows through coil '\(P\)' a magnetic flux of \(10^{-3}~\text{Wb}\) passes through '\(Q\)'. No current is passed through '\(Q\)'. When no current passes through '\(P\)' and a current of \(2~\text{A}\) passes through '\(Q\)', the flux through '\(P\)' is:
1. \( 6.67 \times 10^{-3} ~\text{Wb} \)
2. \( 3.67 \times 10^{-4} ~\text{Wb} \)
3. \( 6.67 \times 10^{-4}~\text{Wb} \)
4. \( 3.67 \times 10^{-3} ~\text{Wb} \)
Subtopic: Mutual Inductance |
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A small circular loop of wire of radius \(a\) is located at the centre of a much larger circular wire loop of radius \({b}.\) The two loops are in the same plane. The outer loop of radius \({b}\) carries an alternating current \({I}={I}_0\cos(\omega \text{t}).\) The emf induced in the smaller inner loop is:
1. \(\frac{\pi \mu_{{o}}{I}_{{o}} {b}^2\omega \cos (\omega {t})}{{a}} \)
2. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \sin (\omega {t})}{{2b}} \)
3. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \sin (\omega {t})}{{b}} \)
4. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \cos (\omega {t})}{{2b}} \)
1. \(\frac{\pi \mu_{{o}}{I}_{{o}} {b}^2\omega \cos (\omega {t})}{{a}} \)
2. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \sin (\omega {t})}{{2b}} \)
3. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \sin (\omega {t})}{{b}} \)
4. \(\frac{\pi \mu_{{o}}{I}_{{o}} {a}^2\omega \cos (\omega {t})}{{2b}} \)
Subtopic: Mutual Inductance |
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- 1(current)
Q. No.
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