A conducting disc of radius r rotates with a small but constant a… - Vidyadip

Question

A conducting disc of radius r rotates with a small but constant angular velocity $\omega$ about its axis. A uniform magnetic field B exists parallel to the axis of rotation. Find the motional emf between the centre and the periphery of the disc.

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Answer

V at a distance $\frac{\text{r}}{2}$
From the centre $=\frac{\text{r}\omega}{2}$
$\text{E}=\text{BlV}$
$\Rightarrow\text{E}=\text{B}\times\text{r}\times\frac{\text{r}\omega}{2}=\frac{1}{2}\text{B}\text{r}^2\omega$

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