Answer Happy

Can children be used to generate electricity? Consider turning a swing into an electric generator by building it out of conducting material such that it forms a conducting loop, as shown in the schematic diagram below. у ab х * Z L 2 w 3 The swing rotates around the line 1-4; the swinging motion is described by the time evolution of the angle between the swing and the vertical direction, (1) = A sin(or). For simplicity, we place the swing right on top of the magnetic North Pole, so that the magnetic field, which has magnitude B, points straight upwards. In your answers, enter o as "theta" and @ as "omega" (without the quotation marks). You must indicate multiplication with an asterisk ("*"). For example, A sin() is entered as "A+sin(omega*t)".
In the Cartesian (x, y, z) coordinates shown in the sketch above, the x and y coordinates of the velocity of the bottom edge of the swing are 0x = -A.L.o.cos(ot). cos(A.sin(m. 1)) Vy = A.L.o.cos(0.1) .sin(A.sin(o . 1)). Derive an expression for the magnitude of the Lorentz force on a charge q in the bottom side of the swing, i.e. between points 2 and 3. FL = The Lorentz force separates charges in the conductor that forms the bottom side of the swing, and the separated charges form an electric field. Derive an expression for the magnitude of this electric field when equilibrium is reached, i.e. when no further charges are separated. E = Hence derive an expression for the voltage between points 2 and 3 of the swing as a Function of time. V23 =