The magnetic field in a region is given by B=B0y/L κ,where L is the fixed length.A conducting rod of length along Y axis between the origin and the point (0,L,0).
If the rod moves with velocity v=v0 î,find the emf induced between the end of rod.
At (0, y, 0) consider length dy of the rod,
\(\begin{gathered} dE = B{v_0}dy = \frac{{{B_0}y}}
{L}{v_0}dy \hfill \\
\therefore E = \int\limits_0^L {\frac{{{B_0}y}}
{L}{v_0}dy = \frac{{{B_0}{v_0}}}
{L}} \int\limits_0^L {ydy} = \frac{{{B_0}{v_0}}}
{L}\frac{{{L^2}}}
{2} = \frac{{{B_0}{v_0}L}}
{2} \hfill \\
\end{gathered} \)
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