In a uniform magnetic field with an induction of 0.5 T, the driving circuit rotates uniformly with an area

In a uniform magnetic field with an induction of 0.5 T, the driving circuit rotates uniformly with an area of 5 * 10 ^ (- 2) m2 and a resistance of 0.1 Ohm. The axis of rotation lies in the plane of the contour and is perpendicular to the line of magnetic induction. Determine the maximum power required to rotate the circuit with an angular velocity of 50 rad / s

To determine the value of the maximum power required to rotate a given circuit, we use the formula: Pmax = U ^ 2 / R = εi ^ 2 / R = (-dF / dt) ^ 2 / R = (-B * S * cosφ / dt) ^ 2 / R = (-B * S * cos (ω * t) / dt) ^ 2 / R = (B * S * ω * sin (ω * t)) ^ 2 / R = (B * S * ω ) ^ 2 / R, since Pmax will be at sin (ω * t) = 1.

Constants and variables: B – field induction (B = 0.5 T); S is the area of a given contour (S = 5 * 10 ^ -2 m2); ω – angular velocity of the contour (ω = 50 rad / s); R – resistance (R = 0.1 Ohm).

Calculation: Pmax = (B * S * ω) ^ 2 / R = (0.5 * 5 * 10 ^ -2 * 50) ^ 2 / 0.1 = 15.625 W.

Answer: For rotation of a given circuit, the maximum power is 15.625 W.