Question

An electromagnet that has a mass of almost 8.0 × 106 kg was built at the CERN particle physics research facility in Switzerland. As part of the detector in one of the world’s largest particle accelerators, this magnet creates a fairly large magnetic field with a magnitude of 0.50 T. Consider a coil of wire that has 880 equal turns. Suppose this loop is placed perpendicular to the magnetic field, which is gradually decreased to zero in 12 s. If an emf of 147 V is induced, what is the area of the coil?

Answer 1

To determine the area of the coil, Faraday's Law is used with the given values of a changing magnetic field, time interval, number of turns and induced emf, resulting in an area of 0.4 square meters.

Step-by-step explanation:

To find the area of the coil, we use Faraday's Law of electromagnetic induction, which states that the induced electromotive force (emf) in a coil is equal to the negative change in magnetic flux (ΔΦ) per unit time (t) multiplied by the number of turns (N) in the coil.

The formula for the induced emf based on Faraday's Law is:

E = -N * (ΔΦ / Δt)

Here, ΔΦ is the change in magnetic flux, which is equal to the change in the magnetic field (ΔB) multiplied by the area (A) of the coil, since the coil is perpendicular to the magnetic field.

Therefore, the change in magnetic flux is:

ΔΦ = ΔB * A

Given that the magnetic field (B) changes from 0.50 T to 0 T in 12 s, ΔB is 0.50 T, and the time interval (Δt) is 12 s. The number of turns (N) is 880, and the induced emf (E) is 147 V. We can rearrange Faraday's Law to solve for the area (A) as follows:

A = E * Δ2t / (N * ΔB)

Plugging in the values:

A = 147 V * 12 s / (880 turns * 0.50 T)

After calculating, we find that the area of the coil is:

A = 0.4 m²

Since we only consider the magnitude, we do not need to worry about the negative sign in Faraday's Law indicating the direction of the induced emf as per Lenz's Law.