Final answer:
The induced emf in a rotating coil within a magnetic field can be calculated using Faraday's Law. The current depends on the emf and the resistance of the coil, which can be determined through Ohm's Law if not given.
Step-by-step explanation:
To solve this physics problem involving electromagnetic induction in a rotating coil within a magnetic field, we apply Faraday's Law of electromagnetic induction. Faraday's Law states that the induced emf (ε) in a coil with N turns rotating in a magnetic field B is given by the rate of change of magnetic flux (Φ) through the coil.
Firstly, we calculate the maximum emf induced using Faraday's Law:
- ε = -N * dΦ/dt
- Φ = B * A * cos(ωt)
The rate of change of magnetic flux dΦ/dt is therefore the derivative of B * A * cos(ωt) with respect to time.
To determine the current in the coil, we use Ohm's Law:
where I is the current and R is the resistance of the coil.
The magnetic flux through the coil at any moment is given by the equation Φ = B * A * cos(θ), where θ is the angle between the magnetic field and the normal to the surface of the coil.
Finally, to obtain the resistance of the coil, the induced emf and current can be used with Ohm's Law:
It's important to note that the actual calculation would depend on the resistance provided or any additional circuit elements present.