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1. | directly proportional to \(i\). |

2. | directly proportional to \(R\). |

3. | directly proportional to \(R^2\). |

4. | Zero. |

Subtopic: Magnetic Flux |

58%

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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 |

58%

From NCERT

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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 |

73%

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A conducting rod of length \(2l\) is rotating with constant angular speed \(\omega\) about its perpendicular bisector. A uniform magnetic field \(\vec {B}\) exists parallel to the axis of rotation. The emf 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 |

60%

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A conductor *ABOCD* moves along its bisector with a velocity of \(1\) m/s through a perpendicular magnetic field of \(1~\text{wb/m}^2\), 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 |

72%

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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 |

75%

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

1. \(V_{A} - V_{O} = \dfrac{B \omega l^{2}}{2}\)

2. \(V_{O} - V_{C} = \dfrac{7}{2} B \omega l^{2}\)

3. \(V_{A} - V_{C} = 4 B \omega l^{2}\)

4. \(V_{C} - V_{O} = \dfrac{9}{2} B \omega l^{2}\)

Subtopic: Motional emf |

58%

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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 |

59%

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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 \(t=0\), then which graph best depicts emf?

* *

1. | 2. | ||

3. | 4. |

Subtopic: Motional emf |

59%

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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 \(\omega\). The maximum value of the emf induced in it is:

1. \(\frac{NBA}{\omega}\)

2. \(NBAω\)

3. \(\frac{NBA}{\omega^{2}}\)

4. \(NBAω^{2}\)

Subtopic: Faraday's Law & Lenz Law |

88%

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