A bicycle rests on its stand oriented in the east-west direction, and its rear wheel rotates at an angular speed of 100 revolutions per minute. Given that the length of each spoke is 30.0 cm and the horizontal component of the earth's magnetic field is 2.0 10⁻⁵ T , determine the emf induced between the axis and the outer end of a spoke. Neglect the centripetal force acting on the free electrons within the spoke.

Step-by-step solution

The bicycle is oriented in the east-west direction, so the plane of the rear wheel is in the east-west vertical plane. The horizontal component of the earth's magnetic field, B_H , is directed north-south, which is perpendicular to the plane of the wheel. The induced emf e between the axis and the outer end of a spoke is given by the formula: e = 1 2 B_H l^2 Given: B_H = 2.0 10⁻⁵ T = 100 rev/min = 100 2 60 rad/s = 10 3 rad/s l = 30.0 cm = 0.3 m Substituting the values: e = 1 2 (2.0 10⁻⁵) ( 10 3 ) (0.3)^2 e = 1.0 10