A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

1. 6.28 × 10^{-4} T

2. 6.28 x 10^{-2} T

3. 12.56 × 10^{-2 }T

4. 12.56 x 10^{-4} T

1. 6.28 × 10

2. 6.28 x 10

3. 12.56 × 10

4. 12.56 x 10

Subtopic: Magnetic Field due to various cases |

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Given below are two statements:

I: | Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current-carrying conductor only. |

II: | Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q. |

In light of above statements choose the most appropriate answer from the options given below:

1. | I is incorrect and II is correct. |

2. | Both I and II are correct. |

3. | Both I and II are incorrect. |

4. | I is correct and II is incorrect. |

Subtopic: Biot-Savart Law |

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From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of the magnetic field in the inside and outside the region of the wire is:

1. | a linearly increasing function of distance up to the boundary of the wire and then linearly decreasing for the outside region. |

2. | a linearly increasing function of distance r up to the boundary of the wire and then decreasing one with 1/r dependence for the outside region. |

3. | a linearly decreasing function of distance up to the boundary of the wire and then a linearly increasing one for the outside region. |

4. | uniform and remains constant for both regions. |

Subtopic: Ampere Circuital Law |

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The ratio of the radii of two circular coils is 1 : 2. The ratio of currents in the respective coils such that the same magnetic moment is produced at the centre of each coil is:

1. 4 : 1

2. 2 : 1

3. 1 : 2

4. 1 : 4

Subtopic: Ampere Circuital Law |

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A strong magnetic field is applied along the direction of velocity of an electron. The electron would move along:

1. a parabolic path

2. the original path

3. a helical path

4. a circular path

Subtopic: Lorentz Force |

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A thick current-carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by:

1. | 2. | ||

3. | 4. |

Subtopic: Ampere Circuital Law |

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An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of ${10}^{5}$ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

1. $4\mathrm{\pi}\times {10}^{-20}\mathrm{N}$

2. $8\times {10}^{-20}\mathrm{N}$

3. $4\times {10}^{-20}\mathrm{N}$

4. $8\mathrm{\pi}\times {10}^{-20}\mathrm{N}$

Subtopic: Lorentz Force |

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A uniform conducting wire of length \(12a\) and resistance 'R' is wound up as a current carrying coil in the shape of,

(i) an equilateral triangle of side 'a'

(ii) a square of side 'a'

The magnetic dipole moments of the coil in each case respectively are:

1. $3{\mathrm{Ia}}^{2}\mathrm{and}4{\mathrm{Ia}}^{2}$

2. $4{\mathrm{Ia}}^{2}\mathrm{and}3{\mathrm{Ia}}^{2}$

3. $\sqrt{3}{\mathrm{Ia}}^{2}\mathrm{and}3{\mathrm{Ia}}^{2}$

4. $3{\mathrm{Ia}}^{2}\mathrm{and}{\mathrm{Ia}}^{2}$

Subtopic: Magnetic Moment |

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In the product

\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )\\~~~=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right )\)

For \(q=1\) and \(\vec{v}=2\hat{i}+4\hat{j}+6\hat{k}\)

and \(\vec{F}=4\hat{i}-20\hat{j}+12\hat{k}\)

What will be the complete expression for \(\vec{B}\)?

1. \(8\hat{i}+8\hat{j}-6\hat{k}\)

2. \(6\hat{i}+6\hat{j}-8\hat{k}\)

3. \(-8\hat{i}-8\hat{j}-6\hat{k}\)

4. \(-6\hat{i}-6\hat{j}-8\hat{k}\)

Subtopic: Lorentz Force |

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A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is:

$\left({\mathrm{\mu}}_{0}=4\mathrm{\pi}\times {10}^{-7}\mathrm{T}\mathrm{m}{\mathrm{A}}^{-1}\right)$

1. $3.4\times {10}^{-4}T$

2. $6.28\times {10}^{-5}T$

3. $3.14\times {10}^{-5}T$

4. $6.28\times {10}^{-4}T$

Subtopic: Magnetic Field due to various cases |

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