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A square of side \(L\) meters lies in the \(XY\text-\)plane in a region where the magnetic field is given by \(\vec{B}=B_{0}\left ( 2\hat{i} +3\hat{j}+4\hat{k}\right )\text{T}\) where \(B_{0}\) is constant. The magnitude of flux passing through the square will be:

1. \(2 B_{0} L^{2}~\text{Wb}\)

2. \(3 B_{0} L^{2}~\text{Wb}\)

3. \(4 B_{0} L^{2}~\text{Wb}\)

4. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)$$

Subtopic: Magnetic Flux |

72%

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The adjoining figure shows two different arrangements in which two square wireframes are placed in a uniform magnetic field \(B\) decreasing with time.

The direction of the induced current \(I\) in the figure is:

The direction of the induced current \(I\) in the figure is:

1. | From \(a\) to \(b\) and from \(c\) to \(d\) |

2. | From \(a\) to \(b\) and from \(f\) to \(e\) |

3. | From \(b\) to \(a\) and from \(d\) to \(c\) |

4. | From \(b\) to \(a\) and from \(e\) to \(f\) |

Subtopic: Faraday's Law & Lenz Law |

66%

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Two identical conductors \(P\) and \(Q\) are placed on two frictionless (conducting) rails \(R\) and \(S\) in a uniform magnetic field directed into the plane. If \(P\) is moved in the direction as shown in the figure with a constant speed, then rod \(Q\):

1. | will be attracted toward \(P\). |

2. | will be repelled away from \(P\). |

3. | will remain stationary. |

4. | maybe repelled or attracted towards \(P\). |

Subtopic: Motional emf |

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Two coaxial coils are very close to each other and their mutual inductance is \(5\) mH. If a current \(50\sin(500 t)\) is passed in one of the coils, then the peak value of induced emf in the secondary coil will be:

1. | \(5000\) V | 2. | \(500\) V |

3. | \(150\) V | 4. | \(125\) V |

Subtopic: Mutual Inductance |

75%

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With the decrease of current in the primary coil from \(2\) A to zero in \(0.01\) s, the emf generated in the secondary coil is \(1000~\text{V}\). The mutual inductance of the two coils is:

1. \(1.25\) H

2. \(2.50\) H

3. \(5.00\) H

4. \(10.00\) H

Subtopic: Mutual Inductance |

88%

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A long solenoid has self-inductance \(L\). If its length is doubled keeping total number of turns constant, then its new self-inductance will be:

1. \(\frac{L}{2}\)

2. \(2L\)

3. \(L\)

4. \(\frac{L}{4}\)

Subtopic: Self - Inductance |

61%

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An inductor is connected to a direct voltage source through a switch. Then:

1. | a very large emf is induced in inductor when the switch is closed. |

2. | a large emf is induced when the switch is opened. |

3. | a large emf is induced whether the switch is closed or opened. |

4. | no emf is induced whether the switch is closed or opened. |

Subtopic: LR circuit |

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The magnetic energy stored in a long solenoid of an area of cross-section \(A\) in a small region of length \(L\) is:

1. | \(\dfrac{B^{2} AL}{2\mu_{0}^{2}}\) | 2. | \(\dfrac{AL}{2 \mu_{0}}\) |

3. | \(\dfrac{1}{2} \mu_{0} B^{2} AL\) | 4. | \(\dfrac{B^{2} AL}{2 \mu_{0}}\) |

Subtopic: Self - Inductance |

64%

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Eddy currents are induced when:

1. | A metal block is kept in a changing magnetic field. |

2. | A metal block is kept in a uniform magnetic field. |

3. | A coil is kept in a uniform magnetic field. |

4. | Current is passed in a coil. |

Subtopic: Eddy Current |

80%

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When a conducting wire \(XY\) is moved towards the right, a current flows in the anti-clockwise direction. Direction of magnetic field at point \(O\) is:

1. | parallel to the motion of wire. |

2. | along with \(XY\). |

3. | perpendicular outside the paper. |

4. | perpendicular inside the paper. |

Subtopic: Motional emf |

72%

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