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Q. No.The dimensions of mutual inductance \((M)\) are:
1. \(\left[M^2LT^{-2}A^{-2}\right]\)
2. \(\left[MLT^{-2}A^{2}\right]\)
3. \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\)
4. \(\left[ML^{2}T^{-2}A^{-2}\right]\)
1. \(\left[M^2LT^{-2}A^{-2}\right]\)
2. \(\left[MLT^{-2}A^{2}\right]\)
3. \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\)
4. \(\left[ML^{2}T^{-2}A^{-2}\right]\)
Subtopic: Mutual Inductance |
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An inductor coil of self-inductance \(10~\text{H}\) carries a current of \(1~\text{A}\). The magnetic field energy stored in the coil is:
| 1. | \(10~\text{J}\) | 2. | \(2.5~\text{J}\) |
| 3. | \(20~\text{J}\) | 4. | \(5~\text{J}\) |
Subtopic: Self - Inductance |
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The magnetic field, through a closed loop of conducting wire covering an area of \(100\) cm2, is \(5\times10^{-2}\) T and it is uniform and normal to the area. If the field is switched off in a time of \(10\) ms, the average emf induced is:
| 1. | \(5\) V | 2. | \(0.5\) V |
| 3. | \(0.05\) V | 4. | \(5\times10^{-4}\) V |
Subtopic: Faraday's Law & Lenz Law |
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Given below are two statements:
| Assertion (A): | A small resistor (i.e., a lamp) is usually applied in parallel to the current-carrying coil of an electromagnet. |
| Reason (R): | During switching off, high voltage is induced across the open switch causing sparks and damage to the insulation. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Self - Inductance |
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Two rectangular loops enter into a uniform magnetic field \(B\) with same velocity \(v\) as shown in the figure. \(V_A\) and \(V_B\) are induced emf in two loops respectively, then:
1. \(V_A>V_B\)
2. \(V_B>V_A\)
3. \(V_A=V_B\)
4. none of the above
1. \(V_A>V_B\)
2. \(V_B>V_A\)
3. \(V_A=V_B\)
4. none of the above
Subtopic: Motional emf |
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A straight horizontal wire \(\mathrm{AB}\) of length \(l\) falls from rest under gravity. A uniform horizontal magnetic field \(B\) acts perpendicular to the plane of motion of \(\mathrm{AB}\), as shown. The induced emf across \(\mathrm{AB}\), \(E\), is proportional to:
| 1. | \(B\) | 2. | \(l\) |
| 3. | time, \(t\) | 4. | all of the above |
Subtopic: Motional emf |
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A small square loop of wire of side \(l\) 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 figure. The mutual inductance of the system is:
1. \(\dfrac{2\sqrt{2}\mu _{0}L^{2}}{\pi l}\)
2. \(\dfrac{\mu_{0} \ell^{2}}{2 \sqrt{2} \pi \mathrm{L}} \)
3. \(\dfrac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi \mathrm{L}} \)
4. \(\dfrac{\mu_{0} L^{2}}{2 \sqrt{2} \pi \ell}\)
1. \(\dfrac{2\sqrt{2}\mu _{0}L^{2}}{\pi l}\)
2. \(\dfrac{\mu_{0} \ell^{2}}{2 \sqrt{2} \pi \mathrm{L}} \)
3. \(\dfrac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi \mathrm{L}} \)
4. \(\dfrac{\mu_{0} L^{2}}{2 \sqrt{2} \pi \ell}\)
Subtopic: Mutual Inductance |
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A straight wire \(AB\) of length \(L\) rotates about \(A,\) with an angular speed \(\omega.\) A constant magnetic field \(\mathbf B\) acts into the plane, as shown.
| Assertion (A): | The average induced electric field within the wire has a magnitude of \(\frac12B\omega L.\) |
| Reason (R): | The induced electric field is the motional EMF per unit length, and the motional EMF is \(\frac12B\omega L^2.\) |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Motional emf |
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A square loop of side \(10\) cm is placed vertically in the east-west plane. A uniform magnetic field of \(0.1\) T is set up across the plane of the loop in the northeast direction. The flux linked with the loop is:
| 1. | \(\sqrt2\times10^{-2}\) Wb | 2. | \(\sqrt2\times10^{-3}\) Wb |
| 3. | \(\frac{1}{\sqrt{2}}\times10^{-2}\) Wb | 4. | \(\frac{1}{\sqrt{2}}\times10^{-3}\) Wb |
Subtopic: Magnetic Flux |
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When the current in a certain coil changes at a rate of \(3~\text{A/s},\) an induced EMF of \(7~\text{mV}\) is observed in a nearby coil. What is the mutual inductance of this arrangement?
1. \(0.33~\text{mH}\)
2. \(1.66~\text{mH}\)
3. \(2.00~\text{mH}\)
4. \(2.33~\text{mH}\)
1. \(0.33~\text{mH}\)
2. \(1.66~\text{mH}\)
3. \(2.00~\text{mH}\)
4. \(2.33~\text{mH}\)
Subtopic: Mutual Inductance |
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