In a uniform magnetic field with an induction of 2 T, a straight horizontal wire with a mass of 2 kg moves

In a uniform magnetic field with an induction of 2 T, a straight horizontal wire with a mass of 2 kg moves vertically upward, through which a current of 4A flows. 3s after the start of movement, the conductor has a speed of 10 m / s. Determine the length of the conductor if the magnetic field induction is directed at an angle of 30º to the vertical.

To calculate the value of the length of a moving conductor, we project all the forces onto the axis of its motion: m * a = m * V / t = Fa – Fт = B * l * I * sinα – m * g, from where we express: B * l * I * sinα = m * V / t – m * g and l = (m * V / t + m * g) / (B * I * sinα).

Constants and variables: m is the mass of the moving conductor (m = 2 kg); V is the speed of the conductor (V = 10 m / s); t – time (t = 3 s); g – acceleration of gravity (g = 9.81 m / s2); B – field induction (B = 2 T); I – current (I = 4 A); α is the angle between the lines of induction and the taken conductor (current).

Calculation: l = (m * V / t + m * g) / (B * I * sinα) = (2 * 10/3 + 2 * 9.81) / (2 * 4 * sin 30º) = 6.57 m.

Answer: The length of the moving conductor is 6.57 m.