Consider a quarter circular conducting ring of large radius r with its centre at the origin, where a magnetic dipole of moment $\vec{m}$ is placed as shown in the figure. If the ring rotates at a constant angular velocity $ω$ about the y-axis, then magnitude of electromotive force inducted between its ends is $n \frac{μ_{0} ω m}{π r}, f i n d n$

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$d e = \vec{v} \times ({\vec{B}}_{r} + {\vec{B}}_{t}) . d \vec{l} = (\vec{v} \times {\vec{B}}_{r}) . d \vec{l} + (\vec{v} \times {\vec{B}}_{t}) . d \vec{l} d e = - v B_{r} d l d e = - ω r \sin θ (\frac{μ_{0}}{4 π .} \frac{2 ω \cos θ}{r^{3}}) d l \begin{array}{l} |d e| = \frac{μ_{0} ω m}{2 π r^{2}} d l \sin θ \cos θ = \frac{μ_{0} ω m}{2 π r} \sin θ d θ . \cos θ \end{array} e = \int | d e | = \frac{μ_{0} ω m}{4 π r} \int_{0}^{π / 2} \sin 2 θ d θ e = \frac{μ_{0} ω m}{4 π r} \frac{{[- \cos 2 θ]}_{0}^{π / 2}}{2} = \frac{μ_{0} ω m}{4 π r}$

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