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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. | \(\dfrac{\pi \mu_{0} R^{2} N \omega I_{0}}{L}\) |
Subtopic: Self - Inductance |
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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. | \(B\left(\omega_{1}+\omega_{2}\right) l^{2}\) |
Subtopic: Motional emf |
55%
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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. | \( Brv\) |
Subtopic: Motional emf |
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A rod \(XY\) of length \(l\) is placed in a uniform magnetic field \(B\), as shown in the diagram. The rod moves with a velocity \(v\), making an angle of \(60^\circ\) with its length. The emf induced in the rod is:
| 1. | \(vBl\) | 2. | \(\dfrac{vBl}{2}\) |
| 3. | \(\dfrac{\sqrt 3}{2}vBl\) | 4. | \(\dfrac{1}{\sqrt 3}vBl\) |
Subtopic: Motional emf |
73%
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An inductor \((L)\) and a capacitor \((C)\) are connected in a circuit, with the capacitor initially charged to a maximum voltage \(V_{0}\). The switch is now closed. The maximum current in the circuit is:
| 1. | \( \dfrac{V_{0}}{\sqrt{L C}}\) | 2. | \(V_{0}\sqrt{LC}\) |
| 3. | \(V_{0} \sqrt{\dfrac{L}{C}}\) | 4. | \(V_{0} \sqrt{\dfrac{C}{L}}\) |
Subtopic: Self - Inductance |
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An inductor \((L)\) and a resistor \((R)\) are connected in series across a battery of emf \(E,\) and the circuit is switched on. The current rises steadily. The rate of increase of the current \(\left(\text{i.e.,}\dfrac {di} {dt}\right),\) when the voltage drops across the resistor is \(\dfrac{E}{2}\), is given by: \(\dfrac {di} {dt}\) =
| 1. | \(\dfrac{E}{L}\) | 2. | \(\dfrac{E}{2L}\) |
| 3. | \(\dfrac{2E}{L}\) | 4. | \(\dfrac{E}{L}e^{-1}\) |
Subtopic: LR circuit |
84%
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A horizontal square loop of area \(A\) has \(n\) turns of wire. It is immersed in a uniform, rotating magnetic field \(B\) which is initially perpendicular to the plane of the loop. The field rotates with an angular speed \(\omega\) about a diagonal of the loop. The EMF induced across the loop is:
| 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 \(n\omega BA\). |
Subtopic: Motional emf |
58%
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The mutual inductance between the two circuits can be determined by simply letting a current \(i\) flow through one circuit and finding the flux of the magnetic field through the second circuit: \(\phi_{2}=M_{12} i_{1}\), where \(M_{12}\) is the mutual inductance. Using this method, or otherwise determine the mutual inductance \((M)\) between a long straight wire, and a small coplanar loop of the area \(A\), located at a distance \(l\) from the wire. The value of \(M\) is:
| 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. | \(\dfrac{\mu_{0} A^{2}}{2 \pi l^{3}}\) |
Subtopic: Mutual Inductance |
80%
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A metallic rod of length \(3~\text{m}\) rotates with an angular speed of \(4~\text{rad/s}\) in a uniform magnetic field. The field makes an angle of \(30^{\circ}\) with the plane of rotation. The emf induced across the rod is \(72~\text{mV}\). The magnitude of the field is:
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
Subtopic: Motional emf |
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A square wire loop of resistance \(0.5\) \(\Omega\)/m, having a side \(10\) cm and made of \(100\) turns is suddenly flipped in a magnetic field \(B,\) which is perpendicular to the plane of the loop. A charge of \(2\times10^{-4}
\) C passes through the loop. The magnetic field \(B\) has the magnitude of:
1. \(2\times10^{-6} \) T
2. \(4\times10^{-6} \) T
3. \(2\times10^{-3} \) T
4. \(4\times10^{-3} \) T
1. \(2\times10^{-6} \) T
2. \(4\times10^{-6} \) T
3. \(2\times10^{-3} \) T
4. \(4\times10^{-3} \) T
Subtopic: Magnetic Flux |
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