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In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^{–4} T) is maintained. An electron is shot into the field with a speed of 4.8 ×${10}^{6}$ m s^{–1} normal to the field. the radius of the circular orbit is:

(e = 1.6 × 10^{–19} C, ${m}_{e}$ = 9.1×10^{–31} kg)

1.4.2 cm

2. 5.3 cm

3. 4.7 cm

4. 5.2 cm

Subtopic: Lorentz Force |

74%

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A circular coil of \(30\) turns and a radius of \(8.0\) cm carrying a current of \(6.0\) A is suspended vertically in a uniform horizontal magnetic field of magnitude \(1.0\) T. The field lines make an angle of \(60^\circ\) with the normal of the coil. What will be the magnitude of the counter-torque that must be applied to prevent the coil from turning?

1. \(7.12\) N-m

2. \(3.13\) N-m

3. \(6.50\) N-m

4. \(4.44\) N-m

Subtopic: Current Carrying Loop: Force & Torque |

75%

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Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A, coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. The magnitude and direction of the net magnetic field due to the coils at their centre is:

1. \(2 \pi \times 10^{-4}\text{ T (East)}\)

2. \(5 \pi \times 10^{-4}\text{ T (East)}\)

3. \(5 \pi \times 10^{-4}\text{ T (West)}\)

4. \(4 \pi \times 10^{-4}\text{ T(West)}\)

Subtopic: Magnetic Field due to various cases |

50%

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For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, \(B=\frac{\mu_0 I R^2 N}{2\left(x^2+R^2\right)^{\frac{3}{2}}}\)

The magnetic field at the centre of the coil is:

1. \(\frac{\mu_0 I N}{R}\)

2. \(\frac{2 \mu_0 I N}{R}\)

3. \(0\)

4. \(\frac{\mu_0 I N}{2 R}\)

Subtopic: Magnetic Field due to various cases |

75%

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A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, the magnetic field inside the core of the toroid is:

1. 3×10^{-2} T

2. 0

3. 2×10^{-3 }T

4. 1×10^{-2} T

Subtopic: Magnetic Field due to various cases |

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An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with a uniform magnetic field of 0.15 T. if the field is transverse to its initial velocity, the radius of the circular path is:

1. 2.10 mm

2. 0.11 mm

3. 1.01 mm

4. 0.12 mm

Subtopic: Lorentz Force |

55%

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A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

1.\(3.14 \times 10^{-4} \ T\)

2.\(2.12 \times 10^{-4} \ T\)

3.\(1.41 \times 10^{-4} \ T\)

4.\(2.01 \times 10^{-4} \ T\)

Subtopic: Magnetic Field due to various cases |

75%

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A long straight wire carries a current of \(35\) A. The magnitude of the magnetic field at a point \(20\) cm from the wire is:

1. \(3.5 \times 10^{-6} \) T

2. \(3.5 \times 10^{-5} \) T

3. \(4.5 \times 10^{-6} \) T

4.\(4.5 \times 10^{-5} \) T

Subtopic: Magnetic Field due to various cases |

78%

From NCERT

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A long straight wire in the horizontal plane carries a current of 50 A in the north to south direction. The magnitude and direction of the magnetic field at a point 2.5 m east of the wire is:

1. \(4 \times 10^{-6}~ T\) vertically upward

2. \(4 \times 10^{-6} ~T\) vertically downward

3. \(3 \times 10^{-6} ~T\) vertically upward

4. \(3 \times 10^{-6} ~T\) vertically downward

Subtopic: Magnetic Field due to various cases |

65%

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A horizontal overhead power line carries a current of \(90\) A in the east to west direction. What is the magnitude and direction of the magnetic field due to the current \(1.5\) m below the line?

1. \(1.2 \times 10^{-5}\) T, towards north

2. \(2.1 \times 10^{-5}\) T, towards south

3. \(1.2 \times 10^{-5}\) T, towards south

4. \(2.1 \times 10^{-5}\) T, towards north

Subtopic: Magnetic Field due to various cases |

60%

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