Q. No.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.
\(\dfrac{1}{\sqrt 3}vBl\)
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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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A rectangular loop of resistance \(R\) is placed in a region where there is a magnetic field \(B\), passing perpendicularly through the plane of the loop, as shown in the figure. The loop is pulled with a constant velocity \(v\) so that it is partially within the field.
| Assertion (A): | An external force \(F\) is needed to be applied in the direction of the velocity \(v\) so that the loop can move with constant velocity \(v\). |
| Reason (R): | As the loop moves towards the right, the magnetic flux decreases inducing an emf and a corresponding current. This current causes a retarding force to be exerted on the wire. |
| 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). |
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Then:
| 1. | \(a=g\) |
| 2. | \(a>g\) |
| 3. | \(a<g\) |
| 4. | \(a\) is initially less than \(g\), but later it is greater than \(g\). |
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The current through the circuit is \(i\). Then:
1. \(i= CBlg\)
2. \(i> CBlg\)
3. \(i < CBlg\)
4. \(i= 0\)
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