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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.
\(\left[ML^{2}T^{-2}A^{-2}\right]\)
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 in the figure. 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 \(\ell \) 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 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 \(\dfrac12B\omega L.\) |
| Reason (R): | The induced electric field is the motional EMF per unit length, and the motional EMF is \(\dfrac12B\omega L^2.\) |
| 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 with a side length of \(10~\text{cm}\) is placed vertically in the east-west plane. A uniform magnetic field of \(0.1~\text{T}\) is applied across the plane of the loop in the northeast direction. The magnetic flux linked with the loop is:
| 1. | \(\sqrt2\times10^{-2}\) Wb | 2. | \(\sqrt2\times10^{-3}\) Wb |
| 3. | \(\dfrac{1}{\sqrt{2}}\times10^{-2}\) Wb | 4. | \(\dfrac{1}{\sqrt{2}}\times10^{-3}\) 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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