A conducting circular loop is placed in a uniform magnetic field 0.04 ~T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mms ⁻¹ . The induced emf in the loop when the radius is 2 ~cm is

Step-by-step solution

Key Idea According to Faraday's second law of electromagnetic induction the induced emf is given by rate of change of magnetic flux linked with the circuit. Here, B=0.04 ~T and - dr dt =2 mms ⁻¹ Induced emf, e = - d dt = - BdA dt =- B d ( r ^2 ) dt =- B 2 r dr dt Now, if r =2 ~cm aligned e & =-0.04 2 2 10⁻² 2 10⁻³ & =3.2 V aligned