A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm . The magnetic field of earth in that region is 0 . 5 G and angle of dip is 30 ° . The emf induced across the blades is N π × 10 - 5 V . The value of N is _______.

Step-by-step solution

Component of the magnetic field perpendicular to the plane of fan blades, B v = B sin 30 ° = 0 . 5 × 10 - 4 T × 1 2 = 1 4 × 10 - 4 T Angular frequency, ω = 2 π × f = 2 π 60 × 1200 rad s - 1 = 40 π rad s - 1 Therefore, induced EMF ε = 1 2 B V ω l 2 = 1 2 × 1 4 × 10 - 4 × 40 π × 0 . 8 2 = 32 π × 10 - 5 V