Question

The area of a 100 turn coll oriented with its plane perpendicular to a 0.15 T magnetio field is 5. 8×10⁻² m2. Find the average induced emf in this coil if the magnetic field reverses its direction in 0.18 s. Express your answer using two significant figures.

Answer 1

The average induced electromagnetic force (emf) in the coil with a 100 turn, an area of 5.8 × 10⁻² m², and a magnetic field reversing from 0.15 T to -0.15 T in 0.18 s is approximately -97 V.

Step-by-step explanation:

The subject of this question is Physics, and it involves calculating the average induced electromotive force (emf) in a coil that is experiencing a change in magnetic flux due to a reversal of the magnetic field. The formula for induced emf (ε) is given by Faraday's law of electromagnetic induction as ε = -N (ΔΦB / Δt), where N is the number of turns in the coil, ΔΦB is the change in magnetic flux, and Δt is the change in time.

Given that the coil has 100 turns (N = 100) and the area of the coil (A) is 5.8 × 10⁻² m². The magnetic field (B) changes from 0.15 T to -0.15 T, so the total change in magnetic field is 0.15 T - (-0.15 T) = 0.30 T. Since the change in magnetic flux (ΔΦB) is equal to the product of the change in magnetic field and the area of the coil (B×A), we get ΔΦB = 0.30 T × 5.8 × 10⁻² m². The change in time (Δt) is 0.18 s.

Now, we can calculate the average induced emf using the formula:

• ε = -N (ΔΦB / Δt)

Substituting the given values:

• ε = -100 (0.30 T × 5.8 × 10⁻² m² / 0.18 s)

Calculating this gives us:

• ε = -96.7 V

However, the question asks for the answer in two significant figures, so the final answer is:

• ε = -97 V

The negative sign indicates the direction of the induced emf according to Lenz's Law, which states that the induced emf will oppose the change in magnetic flux.