Final answer:
To calculate the induced emf E when a magnetic field decreases uniformly to zero over time t, use Faraday's Law of Electromagnetic Induction and express the induced emf as E = A·B/t, where A is the area through which the field is applied. With A equal to the product of sides x and y, the induced emf is E = xy·B/t.
Step-by-step explanation:
To find the magnitude E of the induced emf when a magnetic field decreases uniformly to zero over a time interval t, we can make use of Faraday's Law of Electromagnetic Induction. The law states that the magnitude of the induced emf is equal to the rate of change of the magnetic flux through the loop. Assuming we have an area A within the magnetic field, the change in magnetic flux is ΔΦ = B·A, where B is the initial magnetic field strength.
As the magnetic field decreases uniformly to zero, we can express this rate of change as ΔB/Δt, and since the area A is not changing, ΔΦ/Δt = A·ΔB/Δt. If the entire change in the magnetic field is from B to zero over time t, the average rate of change would be B/t. Hence, the magnitude of the induced emf E is given by:
E = A·B/t
To complete this in terms of the variables x, y, and t, we would need to know how the area A relates to these variables. For example, if A is the area of a rectangle with sides x and y, then A = xy and the magnitude E can be expressed as:
E = xy·B/t