Final answer:
To determine the angular velocity of the coil, we use the formula for maximum emf induced in a rotating coil, which is dependent on the number of turns, the area of the coil, the strength of the magnetic field, and the angular velocity. Given the maximum emf, the number of turns, the dimensions of the coil, and the magnetic field strength, we can solve for the angular velocity.
Step-by-step explanation:
The question is asking for the angular velocity of a rotating square coil in a magnetic field when the maximum electromotive force (emf) is known. The formula for the maximum emf (€max) induced in a rotating coil with N turns, area A, magnetic field strength B, and angular velocity ω is given by €max = NABω, where A is the area of the square coil (side length squared). We'll solve for ω using the given values: N = 24 turns, side length of the coil = 0.16 m and therefore A = (0.16 m)2, B = 0.05 T, and €max = 30 mV = 0.03 V.
To find the angular velocity, we rearrange the formula to ω = €max / (NAB). Substituting the given values, we have ω = 0.03 V / (24 × (0.16 m)2 × 0.05 T). Calculating ω gives us the angular velocity in radians per second (rad/s).