Question

What is the general formula for induced emf of a conducting rod moving on a pi-shaped conductor?

Answer 1

Explanation:

1. When a conductor moves as it cuts through the lines of magnetic flux, a potential difference is induced in that conductor. This phenomenon is referred as the induced emf in a moving conductor rod.
2. Let the magnetic flux density across the rod is ‘$\mathrm{B}$’.
3. The length of the conductor be ‘$\mathrm{l}$’.
4. The conductor moves with a velocity ‘$\mathrm{v}$’.
5. Let, $\mathrm{\theta }$ be the angle between the magnetic field and the direction of motion of the rod.
6. The amount of flux crossing through the rod will be equal to the amount of induced emf produced in the rod. Let the induced emf produced in the straight rod is$=\mathrm{e}$.
   Therefore it can be written that
   $\Rightarrow \mathrm{e}=\mathrm{Blvsin\theta }$
   In the vector form, the above equation can be written as
   $\Rightarrow \mathrm{e}=\overrightarrow{\mathrm{B}}.(\overrightarrow{\mathrm{I}}\times \overrightarrow{\mathrm{V}})$

Therefore, the general formula for induced emf of a conducting rod moving on a pi-shaped conductor is $\mathrm{e}=\overrightarrow{\mathrm{B}}.(\overrightarrow{\mathrm{I}}\times \overrightarrow{\mathrm{V}})$.