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A circular loop of radius R carrying current i lies in the x-y plane. If the centre of the loop coincides with the origin, then the total magnetic flux passing through the x-y plane will be:

1. | directly proportional to I. |

2. | directly proportional to R. |

3. | directly proportional to R^{2}. |

4. | Zero. |

Subtopic: Magnetic Flux |

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A uniform but time-varying magnetic field *B*(*t*) exists in a circular region of radius *a* and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point *P* at a distance *r* from the centre of the circular region:

1. is zero

2. decreases as $\frac{1}{r}$

3. increases as *r*

4. decreases as $\frac{1}{{r}^{2}}$

Subtopic: Faraday's Law & Lenz Law |

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Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:

1. | maximum in the situation (A). |

2. | maximum in the situation (B). |

3. | maximum in the situation (C). |

4. | the same in all situations. |

Subtopic: Mutual Inductance |

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A conducting rod of length 2*l* is rotating with constant angular speed *$\omega $* about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is:

** **

1. \(B\omega l^2\)

2. $\frac{1}{2}B\omega {l}^{2}$

3. $\frac{1}{8}B\omega {l}^{2}$

4. Zero

Subtopic: Motional emf |

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A conductor *ABOCD* moves along its bisector with a velocity of 1 *m/s* through a perpendicular magnetic field of \(1~\mathrm{wb/m^2}\), as shown in fig. If all the four sides are of 1 *m* length each, then the induced emf between points *A* and *D* is:

1. 0

2. 1.41 *volt *

3. 0.71 *volt*

4. None of the above

Subtopic: Motional emf |

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A wire *cd* of length *l* and mass *m* is sliding without friction on conducting rails *ax* and *by* as shown. The vertical rails are connected to each other with a resistance *R* between *a* and *b*. A uniform magnetic field *B* is applied perpendicular to the plane *abcd* such that *cd* moves with a constant velocity of:

1. | \({mgR \over Bl}\) | 2. | \({mgR \over B^2l^2}\) |

3. | \({mgR \over B^3l^3}\) | 4. | \({mgR \over B^2l}\) |

Subtopic: Motional emf |

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A conducting rod *AC* of length 4*l* is rotated about point *O* in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. If *AO* = *l* and *OC* = 3*l, t*hen:

1. ${V}_{A}-{V}_{O}=\frac{B\omega {l}^{2}}{2}$

2. ${V}_{O}-{V}_{C}=\frac{7}{2}B\omega {l}^{2}$

3. ${V}_{A}-{V}_{C}=4B\omega {l}^{2}$

4. ${V}_{C}-{V}_{O}=\frac{9}{2}B\omega {l}^{2}$

Subtopic: Motional emf |

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The graph gives the magnitude \(B(t)\) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first:

1. | \(b > (d = e) < (a = c)\) |

2. | \(b > (d = e) > (a = c)\) |

3. | \(b < d < e < c < a\) |

4. | \(b > (a = c) > (d = e)\) |

Subtopic: Faraday's Law & Lenz Law |

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A square loop of side 5 *cm* enters a magnetic field with 1 *cms ^{-1}*. If the front edge enters the magnetic field at

1. | 2. | ||

3. | 4. |

Subtopic: Motional emf |

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A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega}$. The maximum value of the emf induced in it is:

1. $\frac{\mathrm{NBA}}{\mathrm{\omega}}$

2. $\mathrm{NBA\omega}$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega}}^{2}}$

4. ${\mathrm{NBA\omega}}^{2}$

Subtopic: Faraday's Law & Lenz Law |

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