Final answer:
The angular frequency is 100π rad/s, the amplitude of the induced emf is 800π^2 V, and the expression for circuit current would be I = ε_max/R, with R being the resistance of the semicircular wire.
Step-by-step explanation:
The student has asked about the various aspects related to Faraday's law of electromagnetic induction. Specifically, they want to calculate the angular frequency, the amplitude of the induced electromotive force (emf), and an expression for the circuit current for a semicircular wire rotating in a magnetic field. Here are the calculations:
- a) Angular frequency (ω) can be calculated using the formula ω = 2πf, where f is the frequency. Since the frequency provided is 50 Hz, the angular frequency would be ω = 2π(50 Hz) = 100π rad/s (using π = 3).
- b) Amplitude of the induced emf (ε_max) can be found using Faraday's law, which in this case is ε_max = ωB(r^2)π, where r is the radius, and B is the magnetic field strength. Substituting the given values, ε_max = 100π(4 T)(2 cm^2)π = 800π^2 V (with π = 3 and 1 cm = 0.01 m).
- c) Expression for circuit current (I) can be derived using Ohm's law, I = ε_max/R, where R is the resistance. Assuming the resistance of the wire needs to be provided, the expression would have R as a variable.