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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction

As shown in the figure, a uniform magnetic field B is present within a cylindrical region having a radius of 10 cm . A uniform wire with a length of 80 cm and a resistance of 4.0 is shaped into a square frame and positioned such that one of its sides lies along a diameter of the cylindrical region. Determine the current induced in the frame if the magnetic field increases at a constant rate of 0.010 T/s .

Options

  1. A3.9 10⁻⁵ A
  2. B1.0 10⁻⁴ A
  3. C1.6 10⁻⁴ A
  4. D7.9 10⁻⁵ A

Correct answer

A. 3.9 10⁻⁵ A

Step-by-step solution

Length of the wire, l = 80 cm = 0.8 m Side of the square frame, a = l 4 = 20 cm = 0.2 m Radius of the cylindrical magnetic region, r = 10 cm = 0.1 m Since the side of the square frame ( 20 cm ) is equal to the diameter of the cylindrical region ( 2r = 20 cm ) and one side lies along the diameter, the portion of the frame inside the magnetic field is exactly a semicircle. Effective area of the frame linked with the magnetic field, A = 1 2 r^2 A = 1 2 (0.1)^2 = 0.005 m ^2 According to Faraday's law of induction, the

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