To determine the electromotive force (emf) developed across the ends of the rotating rod, we can use the concept of motional emf generated in a rotating conductor in a magnetic field.
The formula for the motional emf in a rotating rod is given by:
ε=BωL2where:
B is the magnetic field strength
ω is the angular velocity
L is the length of the rotating rod
First, let's find the angular velocity
ω. The frequency
f is given as 100 Hz . The relationship between angular velocity
ω and frequency
f is:
ω=2πf Plugging in the values:
ω=2π⋅100=200πrad∕ sThe length of the rod
L is given as 2 m and the magnetic field strength
B is given as 2 T .
Now, substituting these values into the motional emf formula:
ε=⋅2⋅200π⋅(2)2 Simplifying this expression:
ε=⋅2⋅200π⋅4ε=800π∨Therefore, the emf developed across the ends of the rod is:
Option A:
800π volt