Q. No.A long solenoid of length \(L\), having turns \(N \) and of radius of cross-section \(R\) has a single circular wire wound around it tightly, making a single turn. A current \(i=I_o\sin\omega t\) is passed through this outer wire. The peak EMF induced across the ends of the inner solenoid is (nearly), in magnitude,
| 1. | \(\dfrac{\pi \mu_{0} R^{2} N^{2} \omega I_{0}}{L}\) |
| 2. | \(\dfrac{\mu_{0} R^{2} \omega I_{0}}{N L}\) |
| 3. | \(\dfrac{\pi \mu_{0} L^{2} N \omega I_{0}}{R}\) |
| 4. | \(\dfrac{\pi \mu_{0} R^{2} N \omega I_{0}}{L}\) |
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Two identical conducting rods \(OP,OQ\) of length \(l\) each, rotate about \(O\) in the plane, as shown, with angular velocities \(\omega_{1}\), \(\omega_{2}\). There is a uniform magnetic field \(B\) acting into the plane. The magnitude of the potential difference \((V_P-V_Q)\) is:
| 1. | \(\dfrac{1}{2} B\left(\omega_{1}-\omega_{2}\right) l^{2}\) |
| 2. | \(B\left(\omega_{1}-\omega_{2}\right) l^{2}\) |
| 3. | \(\dfrac{1}{2} B\left(\omega_{1}+\omega_{2}\right) l^{2}\) |
| 4. | \(B\left(\omega_{1}+\omega_{2}\right) l^{2}\) |
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A circular ring is falling in a vertical plane, in a uniform horizontal magnetic field \((B)\) which passes perpendicular to the plane of the ring. \(P\) is the highest point, while \(S\) is the left-most point of the ring. The potential difference between \(P\) and \(S\) is (when the speed of the ring is \(v\)):
| 1. | \(\text{Zero}\) |
| 2. | \(\sqrt2 Brv\) |
| 3. | \(\dfrac{\pi r^2Bv}{4}\) |
| 4. | \( Brv\) |
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| 1. | \(vBl\) | 2. | \(\dfrac{vBl}{2}\) |
| 3. | \(\dfrac{\sqrt 3}{2}vBl\) | 4. | \(\dfrac{1}{\sqrt 3}vBl\) |
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| 1. | \( \dfrac{V_{0}}{\sqrt{L C}}\) | 2. | \(V_{0}\sqrt{LC}\) |
| 3. | \(V_{0} \sqrt{\dfrac{L}{C}}\) | 4. | \(V_{0} \sqrt{\dfrac{C}{L}}\) |
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| 1. | \(\dfrac{E}{L}\) | 2. | \(\dfrac{E}{2L}\) |
| 3. | \(\dfrac{2E}{L}\) | 4. | \(\dfrac{E}{L}e^{-1}\) |
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| 1. | constant, of magnitude \(n\omega BA\). |
| 2. | increasing with time \(t\), of magnitude \(n\omega^2BAt\). |
| 3. | decreasing with time \(t\), of magnitude \(\dfrac{nBA}{t}\). |
| 4. | sinusoidal with time \(t\), of amplitude \(n\omega BA\). |
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| 1. | \( \dfrac{\mu_{0} l}{2 \pi}\) | 2. | \(\dfrac{\mu_{0} A}{2 \pi l}\) |
| 3. | \(\dfrac{\mu_{0} l^{3}}{4 \pi A}\) | 4. | \(\dfrac{\mu_{0} A^{2}}{2 \pi l^{3}}\) |
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1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
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1. \(2\times10^{-6} \) T
2. \(4\times10^{-6} \) T
3. \(2\times10^{-3} \) T
4. \(4\times10^{-3} \) T
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