Physics - EMI/AC Question with Solution | TestHub

The motional EMF is given by $E=\int (\vec{v}\times \vec{B})\cdot d\vec{l}$. Here, the velocity $\vec{v}$ of any point on the rod is tangential to its circular path, hence perpendicular to the rod's length. The magnetic field $\vec{B}$ is parallel to the axis of rotation, which means $\vec{B}$ is parallel to the length vector $d\vec{l}$ of the rod. Since $\vec{B}$ is parallel to $d\vec{l}$, the cross product $(\vec{v}\times \vec{B})$ will be perpendicular to $d\vec{l}$. Therefore, $(\vec{v}\times \vec{B})\cdot d\vec{l}=0$. Thus, the potential difference developed between the two ends of the rod is zero.