The electromotive force is induced when a coil with the value\({\rm{N}}\)turns experiences a flux change of the value\({\rm{\Delta \Phi }}\)in time\({\rm{\Delta t}}\)is given by:
\({\rm{E = - N}}\frac{{{\rm{\Delta \Phi }}}}{{{\rm{\Delta t}}}}\)……………….(1)
The flux reaches the point zero from the maximal value under the given time, we can simply write the change in flux as:
\(\begin{aligned}{}{\rm{\Delta \Phi = 0 - BA}}\\{\rm{ = - BA}}\end{aligned}\)
The emf then will be:
\({\rm{\varepsilon = }}\frac{{{\rm{NBA}}}}{{\rm{t}}}\)……………………….(2)
Substituting the area such that:
\(\begin{aligned}{}{\rm{A = \pi }}{{\rm{R}}^{\rm{2}}}\\{\rm{ = }}\frac{{{\rm{\pi }}{{\rm{D}}^{\rm{2}}}}}{{\rm{4}}}\end{aligned}\)
Therefore the analytical result is,
\({\rm{\varepsilon = }}\frac{{{\rm{\pi NB}}{{\rm{D}}^{\rm{2}}}}}{{\rm{4}}}\)………………………(3)
The numerical value is then evaluated as:
\(\begin{aligned}{}{\rm{\varepsilon }} &= \frac{{{\rm{\pi \times 1000 \times }}\left( {{\rm{5 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}\;{\rm{T}}} \right){\rm{ \times }}{{\left( {{\rm{0}}{\rm{.2}}\;{\rm{m}}} \right)}^{\rm{2}}}}}{{\rm{4}}}\\ &= {\rm{1}}{\rm{.57\;}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{3}}}}\;{\rm{V}}\left( {\frac{{1\;{\rm{mV}}}}{{{\rm{1}}{{\rm{0}}^{ - {\rm{3}}}}\;{\rm{V}}}}} \right)\\ &= {\rm{1}}{\rm{.57}}\;{\rm{mV}}\end{aligned}\)
Therefore, the average \({\rm{emf}}\) induced is obtained as \({\rm{1}}{\rm{.57}}\;{\rm{mV}}\).
