A rectangular coil of 200 turns has a length of 200 mm and width
120 mm. The coil rotates with a constant angular speed of 1200
revolutions per minute about an axis through the midpoints of its
longer sides in a uniform magnetic field of 2.4 x 10-2 T.
Starting from a time when the coil’s plane is parallel to the
magnetic field, calculate the average induced electromotive
force whilst the coil is turning 1/(2pi) radians.
E(emf) = N x B x w x A x sin (theta)
where N = number of turns
B = magnetic field (T)
A = area of coil
w = angular velocity (rad/s)
theta = angle made by coil wrt perpendicular to the field
The Attempt at a Solution
Angular velocity = 40pi (1200rpm)
As the coil rotates through the field plane the induced emf is at the maximum (sin (theta) = 1)
E = 200 x 2.4 x 10-2 T x 40pi x 0.120m x 0.200m x sin (pi/2) = 14.47V
After rotating towards the vertical through the rather small angle 1/(2pi) radians:
E = 200 x 2.4 x 10-2T x 40pi x .120m x .200m x sin (pi/2 - (1/(2pi)) = 14.29V
The given result is 9.216V so I've obviously missed something. Yet - it seems unusual that after rotating through such a small angle that the induced voltage should fall as low as the given answer.
Help gratefully received!