You want to build a generator for a multiday canoe trip You

You want to build a generator for a multi-day canoe trip. You have a fairly large permanent magnet, some wire, and a lightbulb. You may build it as follows. Wind the wire for about 200 turns into a coil of 15 cm radius. Tape up the coil and place it in the region between the poles of the magnet that produces a 0.10 T magnetic field. Connect a hand crank to the coil and rotate it at a rotational speed .

Suppose we need 6.0 V to light the bulb (the peak voltage). What is the required rotational speed? Express your answer to two significant figures and include the appropriate units.

Solution

angular speed is w = V/(N*A*B)

A is the area of cross section = pi*r^2 = 3.142*0.15^2 = 0.070695 m^2

N = 200 turns

B = 0.1 T

then w = 6/(200*0.1*0.070695) = 4.24 rad/s