Q50. A boat is moving due east in a region where the Earth's magnetic field is 5.0 × 10⁻⁵ NA⁻¹m⁻¹ du

Q: What is the correct answer for CUET UG Physics Q50?

The correct answer is b. When a conductor moves in a magnetic field, a motional electromotive force (emf) is induced across its ends. The magnitude of this induced emf (ε) is given by ε = BLvsinθ, where B is the magnetic field strength, L is the length of the conductor, v is its velocity, and θ is the angle between the velocity vector and the magnetic field vector, and all three vectors (B, L, v) must be mutually perpendi

Q: Q50. A boat is moving due east in a region where the Earth's magnetic field is 5.0 × 10⁻⁵ NA⁻¹m⁻¹ due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boats is…

The correct answer is b. When a conductor moves in a magnetic field, a motional electromotive force (emf) is induced across its ends. The magnitude of this induced emf (ε) is given by ε = BLvsinθ, where B is the magnetic field strength, L is the length of the conductor, v is its velocity, and θ is the angle between the velocity vector and the magnetic field vector, and all three vectors (B, L, v) must be mutually perpendi

Q: What are the options for this CUET UG Physics question?

A. 0.50 mV · B. 0.15 mV · C. 1.00 mV · D. 0.75 mV

Question

Q50. A boat is moving due east in a region where the Earth's magnetic field is 5.0 × 10⁻⁵ NA⁻¹m⁻¹ due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boats is 1.5 ms⁻¹, the magnitude of the induced emf is:
(a) 0.50 mV
(b) 0.15 mV
(c) 1.00 mV
(d) 0.75 mV

FirstInTest · Accepted Answer

When a conductor moves in a magnetic field, a motional electromotive force (emf) is induced across its ends. The magnitude of this induced emf (ε) is given by ε = BLvsinθ, where B is the magnetic field strength, L is the length of the conductor, v is its velocity, and θ is the angle between the velocity vector and the magnetic field vector, and all three vectors (B, L, v) must be mutually perpendicular for the maximum induced emf (sinθ=1). In this problem: The Earth's magnetic field (B) is 5.0 × 10⁻⁵ T, directed horizontally due North. The aerial (conductor) has a length (L) of 2 m and is oriented vertically. The boat's speed (v) is 1.5 m/s, directed horizontally due East. Since North, East, and Vertical are mutually perpendicular directions, the velocity (East), magnetic field (North), and length of the aerial (Vertical) are all perpendicular to each other. Thus, the formula simplifies to ε = BLv. Substituting the values: ε = (5.0 × 10⁻⁵ T) × (2 m) × (1.5 m/s) = (5.0 × 10⁻⁵) × 3 V = 15 × 10⁻⁵ V = 0.00015 V = 0.15 mV. Options (a), (c), and (d) are incorrect values resulting from calculation errors.

Answer

0.50 mV

Answer

0.15 mV

Answer

1.00 mV

Answer

0.75 mV

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