Final answer:
The induced EMF at any instant when the radius of a conducting loop within a magnetic field is shrinking, can be calculated using Faraday's law of electromagnetic induction. This law advises that the induced EMF is dependent on the rate of change of magnetic flux, which is determined by the magnetic field strength, the alteration in area of the loop, and the rate at which this change occurs.
Step-by-step explanation:
In the question, a conducting circular loop is placed in a uniform magnetic field with an induction of b Tesla. The plane of the loop is normal to the field. At the instant when the radius is r, the induced EMF (Electromotive Force) can be determined based on Faraday's law of electromagnetic induction. This law states that the induced emf is equal to the rate of change of magnetic flux.
The flux through the loop in this case is given by Φ = BA, where B is the uniform magnetic field and A is the loop area. As the loop is circular, A = πr^2. Therefore, changing the radius at rate dr/dt will induce an emf. Differentiating the flux with respect to time, we get dΦ/dt = B*d(πr^2)/dt = 2πrB(dr/dt). According to Faraday's law, therefore, the magnitude of the induced emf is equal to the rate of change of flux, i.e., E = dΦ/dt, leading to an induced emf E= 2πrB(dr/dt).
This explanation aligns to the findings from experiments, that the emf produced in a conducting loop is proportional to the rate of change of the product of the perpendicular magnetic field and the loop area. Thus, changing the area induces an emf towards the area which opposes the change.
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