Question

A fixed 16.3-cm-diameter wire coil is perpendicular to a magnetic field 0.46 T pointing up. In 0.28 s , the field is changed to 0.31 T pointing down. What is the average induced emf in the coil?

Answer 1

Electromagnetic induction is a physics phenomenon where a changing magnetic field within a coil of wire induces an electrical current. This is governed by Faraday's Law, which is applied using the coil's dimensions and the given changes in the magnetic field and time to calculate the average induced emf.

Step-by-step explanation:

The subject of your question deals with electromagnetic induction, a phenomenon in physics where a changing magnetic field within a coil of wire induces (or generates) an electric current within the wire. This is governed by Faraday's Law of electromagnetic induction which is defined as: ε = -N ΔΦ/Δt, where ε is the induced emf, N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time.

The area(A) of your coil can be obtained with the formula for the area of a circle, which is A = πr^2, for a radius r=16.3cm/2. After that, you calculate the change in the magnetic field(ΔB), which is the final magnetic field minus the initial: ΔB = -0.31T - 0.46T = -0.77T (The negative sign signifies that the magnetic field reversed direction). The change in the magnetic flux(ΔΦ), then is ΔΦ = A*ΔB. Finally, you can calculate the induced emf(ε) by substituting your given time (0.28s), your calculated ΔΦ, and assume a single loop(N=1), into Faraday's Law.

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