COMEDK 2024 Shift 1 Paper

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=‌

1

2

BωL2
where:
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∕ s
The 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=‌

1

2

⋅2⋅200π⋅(2)2
Simplifying this expression:
ε‌=‌

1

2

⋅2⋅200π⋅4
ε‌=800π∨
Therefore, the emf developed across the ends of the rod is:
Option A: 800π volt