A conducting circular loop is placed in a uniform magnetic field B =0.125 ~T with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of 2 ~mm ~s ⁻¹ , then the induced emf when the radius is 4

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A conducting circular loop is placed in a uniform magnetic field B =0.125 ~T with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of 2 ~mm ~s ⁻¹ , then the induced emf when the radius is 4 ~cm is

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Correct answer: B. 20 V

The magnetic flux through the circular loop is given by = B A = B ( r^2) , where B is the magnetic field and r is the radius of the loop. The induced electromotive force (emf) is given by Faraday's law of induction: = - d dt . Since B is constant, = - d dt (B r^2) = -B (2r dr dt ) = -2 B r dr dt . Given B = 0.125 T , r = 4 cm = 0.04 m , and the rate of shrinking dr dt = -2 mm s ⁻¹ = -2 10⁻³ m s ⁻¹ . Substituting these values into the expression for magnitude of induced emf: | | = 2 (0.125) (0.04) (2 10⁻³) | | = 2 (

A conducting circular loop is placed in a uniform magnetic field B =0.125 ~T with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of 2 ~mm ~s ⁻¹ , then the induced emf when the radius is 4 ~cm is

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