Question

a metal rod with a length of 23.0 cm lies in the xy-plane and makes an angle of 37.5 (degrees) with the positive x-axis and an angle of 52.5(degrees) with the positive y-axis. the rod is moving in the + x-direction with a speed of 6.80 m/s. the rod is in a uniform magnetic field B = (0.180T)i - (0.270T)j - (0.0800T)k.
What is the magnitude of the emf induced in the rod?

Answer 1

\[
\vec{B}=0.18\hat{i}-0.27\hat{j}-0.08\hat{k}\\
\vec{v}=6.8\hat{i}\\
d\vec{l}=\ldots\qquad\text{(find using co-ordinates}
\]
This motion will create a force of
\[\vec{F}=\vec{v}\times\vec{B}\] (vector product)
EMF gets induced in every infinitesimal piece of the conductor
\[E=\int\vec{F}\cdot d{\vec{l}}\]