Final answer:
The peak electromotive force (emf) generated when a 1000-turn coil with a diameter of 21 cm is rotated in the Earth's magnetic field from a position initially perpendicular to the field to one parallel to the field in 11 ms is 248.1 mV.
Step-by-step explanation:
The emf induced in a coil rotating in a magnetic field can be determined by the formula ε = EO sin oot. It is at a maximum where the coil is perpendicular to the magnetic field of the Earth, which is 5.0 x 10^-5 T. In this case, the maximum emf is dictated by the surface area of the coil, number of turns, and the angular velocity of the coil.
Given the diameter of the coil is 21 cm, we can find the radius (r = 0.105 m) and therefore the area of the coil (A = πr^2 = 0.0347 m^2). With 1000 turns and a rotation from perpendicular to parallel in 11ms, the rotation can be understood as a quarter of a revolution, or π/2 radians, in 11 x 10^-3 seconds. This gives the angular velocity (ω) as (π/2) / (11 x 10^-3) = 143.2394 rad/s.
Substituting these values into the formula, we get ε = EOsin(ωt). At its peak, where sin(ωt)=1, the emf is therefore EO=BAωN=5.00x10^-5T x 0.0347m^2 x 143.2394 rad/s x 1000 turns = 0.2481 V = 248.1 mV.
In this case, the coil is rotated from a position perpendicular to the Earth's magnetic field to a position parallel to the field in 11 ms. The maximum emf is given as 3.95681 V. Using these values, we can calculate the peak emf generated in the coil.
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