Final answer:
The magnetic field strength needed to produce a 24.0 V peak emf in the described car generator, rotating at 400 rpm with a 300-turn coil and dimensions of 5.00 by 8.00 cm, is approximately 0.20 Tesla. Therefore, the correct answer is option a) 0.20 T
Step-by-step explanation:
To calculate the magnetic field strength needed to produce a 24.0 V peak emf in a car generator coil rotating at 400 rpm, we need to use Faraday's Law of Induction which states that the induced emf (ε) in a coil is equal to the negative change in magnetic flux (Φ) times the number of turns (N) in the coil.
The formula is ε = -N * dΦ/dt. For a coil rotating in a magnetic field, we express the change in flux as dΦ = B * A * cos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the surface of the coil.
The peak emf occurs when the rate of change of the magnetic flux is the greatest, which is when θ is equal to 90 degrees, making cos(θ) = 0. Therefore, the maximum change in flux over time, which occurs when sin(θ) = 1, will be dΦ/dt = B * A * ω, where ω is the angular velocity of the coil. The coil's area A is 5.00 cm by 8.00 cm or 0.05 m * 0.08 m. To find angular velocity in rad/s, we convert 400 rpm to rad/s by multiplying by 2π/60. The peak emf formula becomes 24.0 V = N * B * A * ω.
After solving for B, the magnetic field strength needed to produce a 24.0 V peak emf with the given parameters turns out to be (b) approximately 0.20 T, which is in the range of magnetic field strengths available in both permanent and electromagnets commonly used in various applications.
Therefore, the correct answer is option a) 0.20 T