Figure shows a conducting disc rotating about its axis in a perpe… - Vidyadip

Question

Figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B. A resistor of resistance R is connected between the centre and the rim. Calculate the current in the resistor. Does it enter the disc or leave it at the centre? The radius of the disc is 5.0cm, angular speed $\omega=10 \ \text{rad/s}, \ \text{B}=0.40\text{T}$ and $\text{R}=10\Omega.$

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Answer

$\text{B}=0.40\text{T},\omega=10 \ \text{rad}/',\text{r}=10\Omega$
$\text{r}=5\text{cm}=0.05\text{m}$
Considering a rod of length 0.05m affixed at the centre and rotating with the same $\omega$.
$\text{V}=\frac{\text{L}}{2}\times\omega=\frac{0.05}{2}\times10$
$\text{e}=\text{BLV}=0.40\times\frac{0.05}{2}\times10\times0.05=5\times10^{-3}\text{V}$
$\text{L}=\frac{\text{e}}{\text{R}}=\frac{5\times10^{-3}}{10}=0.5 \ \text{mA}$
It leaves from the centre.

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