 Motional EMF
Question

# A uniform magnetic field exists in the region given by $\stackrel{\to }{\mathrm{B}}=3\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}+5\stackrel{^}{\mathrm{k}}$ .  A rod of length 5 m placed along Y-axis is moved along X-axis with constant speed $1\text{ }{\mathrm{ms}}^{-1}$ .  Then induced e.m.f in the rod is

Moderate
Solution

## $\mathrm{l}=5\mathrm{j}$$\mathrm{V}=1\mathrm{i}$$\mathrm{e}=\mathrm{B}\left(\mathrm{l}×\mathrm{V}\right)$$=\mathrm{B}\left|\begin{array}{ccc}\stackrel{^}{\mathrm{i}}& \stackrel{^}{\mathrm{j}}& \stackrel{^}{\mathrm{k}}\\ 0& 5& 0\\ 1& 0& 0\end{array}\right|$$=\mathrm{B}\left(0-5\stackrel{^}{\mathrm{K}}\right)$$\left(3\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}+5\stackrel{^}{\mathrm{k}}\right).\left(-5\stackrel{^}{\mathrm{k}}\right)$$=25\mathrm{V}$Conceptual approach:-As the rod is placed along Y axis and moving in x direction, the magnetic field has to be perpendicular to both $\stackrel{\to }{\mathrm{l}}\mathrm{and}\stackrel{\to }{\mathrm{v}}$ in order to develop motional emf. Hence the z component of the magnetic field should be taken.

Get Instant Solutions  