Final answer:
Using Faraday's law and the given numbers, we calculate the change in magnetic flux which then gives us the induced emf. The changing magnetic field creates a change in flux of -16 Wb over 15 seconds, resulting in an induced emf of 1.067 V.
Step-by-step explanation:
The phenomenon described in this question is defined by Faraday's Law of electromagnetic induction. This law tells us that an emf will be induced in a conductor like a wire loop when there is a change in the magnetic field in the area the loop encompasses. Calculating the induced emf involves measuring the change in flux over time.
Magnetic flux (Ф) refers to the magnetic field (B) multiplied by the area (A) it passes through and can be mathematically expressed as Ф = B * A, so we need to first calculate the initial and final flux. Our square loop has an area of 2 m * 2 m = 4 m². So, our initial flux will be 5 T * 4 m² = 20 Weber (Wb) and final flux will be 1 T * 4 m² = 4 Wb.
Next, we'll calculate the change in flux (∆Ф = Ф_final - Ф_initial), which is 4 Wb - 20 Wb = -16 Wb. Faraday's Law states that the absolute value of the change in flux is directly proportional to the induced emf, and we calculate it over time, giving us |emf| = ∆Ф / ∆t = |-16 Wb| / 15 s = 1.067 V. So, the induced emf in the loop is 1.067 V. Remember that - sign here indicates a reversal of the magnetic field direction, rather than a negative value for the induced emf, as no negative energy can be created.
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