Question

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35m x 0.55m. The magnetic field has a magnitude of 2.1T and is inclined at an angle of 65 degrees with respect to the normal to the plane of the loops. (a) If the magnetic field decreases to zero in a time of 0.45s, what is the magnitude of the average emf induced in the loop.

Answer 1

The magnitude of the average emf induced in the loop is 0.73V. This is calculated using Faraday's Law of electromagnetic induction, which states that the induced emf in a loop is equal to the negative rate of change of magnetic flux through the loop.

Step-by-step explanation:

To find the magnitude of the average emf induced in the loop, you would use Faraday's Law of electromagnetic induction. The law states that the induced emf (electromotive force) in a closed loop of wire is equal to the negative rate of change of the magnetic flux through the loop. In mathematical terms, this is expressed as ε = -dΦ/dt, where ε is the induced emf, dΦ is the change in magnetic flux, and dt is the change in time.

The magnetic flux Φ is defined as the product of the magnetic field strength (B), the area of the loop (A), and the cosine of the angle (θ) between the magnetic field and the normal to the plane of the loops. Here B = 2.1T, A = 0.35m x 0.55m = 0.1925m2, and θ = 65 degrees.

The initial magnetic flux is then Φ1 = B x A x cosθ = 2.1T x 0.1925m2 x cos65 =0.33Wb. The final magnetic flux is zero since the magnetic field decreases to zero. Therefore dΦ = Φ2 - Φ1 = 0Wb - 0.33Wb = -0.33Wb.

The time dt = 0.45s. So using Faraday's Law, the average emf ε = -dΦ/dt = -(-0.33Wb / 0.45s) = 0.73V, and the magnitude is 0.73V.

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