A metallic rod of 10‌cm is rotated with a frequency 100 revolution per second about an axis perpendicular to its length and passing through its one end in uniform transverse magnetic field of strength 1T. The emf developed across its ends is:
To calculate the emf developed across the ends of the rod, we can use the formula that relates the emf (ε) to the magnetic field (B), the length of the rod (I), and the angular velocity (ω) of the rotation. The formula is given by: E=B⋅l2⋅ω∕2 Given data: The magnetic field strength, B=1T The length of the rod, l=10‌cm=0.1m (since 1‌cm=0.01m ) The frequency of rotation, f=100 revolutions per second To find the angular velocity (ω), we use the relation between frequency and angular velocity, which is: ω=2πf Substituting the given frequency, ω=2π⋅100=200π‌rad∕s Now, substituting the given values in the emf equation: ‌E=1⋅(0.1)2⋅200π∕2 ‌E=0.01⋅100π ‌E=πV ‌E=3.14V Therefore, the emf developed across the ends of the rod is 3.14V, which corresponds to Option B.