A straight horizontal wire \(\mathrm{AB}\) of length \(l\) falls from rest under gravity. A uniform horizontal magnetic field \(B\) acts perpendicular to the plane of motion of \(\mathrm{AB}\), as shown. The induced emf across \(\mathrm{AB}\), \(E\), is proportional to:

1. \(B\)

2. \(l\)

3. time, \(t\)

4. all of the above

1. \(B\)

2. \(l\)

3. time, \(t\)

4. all of the above

Subtopic: Â Motional emf |

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A rod of length \(l\) rotates with a uniform angular velocity \(\omega\) about its perpendicular bisector. A uniform magnetic field \(B\) exists parallel to the axis of rotation. The potential difference between the two ends of the rod is:

1. zero

2. \(\frac{1}{2}Bl\omega ^{2}\)

3. \(Bl\omega ^{2}\)

4. \(2Bl\omega ^{2}\)

Subtopic: Â Motional emf |

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A conducting rod is moved with a constant velocity \(v\) in a magnetic field. A potential difference appears across the two ends,

a. | \(\overrightarrow v \|\overrightarrow l\) | if

b. | if \(\overrightarrow v \|\overrightarrow B\) |

c. | \(\overrightarrow l \|\overrightarrow B\) | if

d. | none of these |

Choose the correct option:

1. | (a), (b) |

2. | (b), (c) |

3. | (d) only |

4. | (a), (d) |

Subtopic: Â Motional emf |

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A wheel with \(10\) metallic spokes each \(0.5\) m long is rotated with a speed of \(120\) rev/min in a plane normal to the horizontal component of earth’s magnetic field H_{E} at a place. If \(H_E=0.4\) G at the place, what is the induced emf between the axle and the rim of the wheel? (\(1\) G=\(10^{-4}\) T)

1. \(5.12\times10^{-5}\) T

2. \(0\)

3. \(3.33\times10^{-5}\)

4. \(6.28\times10^{-5}\)

Subtopic: Â Motional emf |

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An \(L\)-shaped rod \((ABC;AB=BC=a)\) moves in its own plane with a velocity \(v\) parallel to \(AB.\) There is a uniform magnetic field \(B\) acting into the plane as shown. The emf developed between \(A,C\) is:

1. \(Bav\)

2. \(\sqrt2Bav\)

3. \(\frac{Bav}{2}\)

4. zero

1. \(Bav\)

2. \(\sqrt2Bav\)

3. \(\frac{Bav}{2}\)

4. zero

Subtopic: Â Motional emf |

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A conducting circular wire of radius \(r\) is moving with constant velocity \(v\) towards the right in a uniform magnetic field \(B.\) We consider two points \(X,Y\) such that chord \(XY\) is perpendicular to the velocity \(v\) and is at a distance \(x\) from the centre \((O)\) of the circle. The EMF induced between \(X,Y\) is \(\varepsilon.\) Then, \(\varepsilon\) is proportional to:

1. \(x\)

2. \(\sqrt{r^2-x^2}\)

3. \(r\)

4. \(x\sqrt{r^2-x^2}\)

1. \(x\)

2. \(\sqrt{r^2-x^2}\)

3. \(r\)

4. \(x\sqrt{r^2-x^2}\)

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A straight horizontal wire of mass \(m\) and length \(l,\) and having a negligible resistance can slide freely on a pair of conducting parallel rails, placed vertically. The rails are connected at the top by a capacitor \(C.\) A uniform magnetic field \(B\) exists in the region, perpendicular to the plane of the rails. The wire

1. | falls with uniform velocity. |

2. | \(g\). | accelerates down with acceleration less than

3. | \(g\). | accelerates down with acceleration equal to

4. | moves down and eventually comes to rest. |

Subtopic: Â Motional emf |

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A triangular wire frame, in the form of an equilateral triangle PQR moves with a uniform velocity into a region where there is a uniform magnetic field \(B\). The edge PQ is parallel to the boundary of the region and the velocity \(v\) is perpendicular to it. The emf(\(E\)) induced within the frame is plotted as a function of time \(t,\) starting from when the frame enters the magnetic field. \(E\) is given by:

1. \(Bv^2t\)

2. \(2Bv^2t\)

3. \(\frac{\sqrt3}{2}Bv^2t\)

4. \(\frac{2}{\sqrt3}Bv^2t\)

1. \(Bv^2t\)

2. \(2Bv^2t\)

3. \(\frac{\sqrt3}{2}Bv^2t\)

4. \(\frac{2}{\sqrt3}Bv^2t\)

Subtopic: Â 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. \(vBl \over 2\)

3. \({\sqrt 3 \over 2}vBl\)

4. \({1 \over \sqrt 3}vBl\)

1. \(vBl\)

2. \(vBl \over 2\)

3. \({\sqrt 3 \over 2}vBl\)

4. \({1 \over \sqrt 3}vBl\)

Subtopic: Â Motional emf |

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An emf is generated by an ac generator having \(100\) turn coil, of loop area \(1\) m^{2}. The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of \(0.05\) T perpendicular to the axis of rotation of the coil. The maximum value of emf is:

1. \(3.14\) V

2. \(31.4\) V

3. \(62.8\) V

4. \(6.28\) V

1. \(3.14\) V

2. \(31.4\) V

3. \(62.8\) V

4. \(6.28\) V

Subtopic: Â Motional emf |

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