Question
Physics Question on Electromagnetic induction
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 the angle of dip is 30∘. The emf induced across the blades is Nπ×10−5V. The value of N is \\_\\_\\_\\_\\_.
Step 1. Calculate the Effective Vertical Component of the Magnetic Field:
Given:
B=0.5G=0.5×10−4T
The vertical component of the magnetic field Bv, considering the angle of dip δ=30∘, is:
Bv=Bsinδ=0.5×10−4×sin30∘=0.5×10−4×21=41×10−4T
Step 2. Convert Angular Velocity from rpm to rad/s:
Angular velocity ω in rad/s is given by:
ω=2π×f=2π×601200=2π×20=40πrad/s
Step 3. Determine the Radius of Rotation:
The length of each blade is ℓ=80cm=0.8m. Therefore, the effective radius r of rotation is:
r=0.8m
Step 4. Calculate the Induced emf:
The emf ε induced across the tips of the blades (assuming the emf induced across two opposite ends) is given by:
ε=21Bvωr2
Substituting the values:
ε=21×41×10−4×40π×(0.8)2
Simplifying further:
ε=21×41×10−4×40π×0.64=32π×10−5V
Step 5. Conclude the Value of N:
Comparing with Nπ×10−5V, we find:
N=32