Question

Figure shows a conducting disc rotating about its axis in a perpendicular magnetic field B.A resistance 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 center? The radius of the dise is $5.0$ cm, angular speed T and $\omega =10$ rad/s, B=$0.40$ $T$ and $R$ $10\Omega$.

Answer 1

Magnetic field $B\perp$ to axis of rotation

radius of disc $=5cm$

$\omega =10rad/s$

$B=0.40T$

$R=10\Omega$

Let consider a element arc at a distance x from the centre EMF at dx,

$dE=BdxV$ $|v=x\omega$

$=Bxwdx$

$\int de={\int }_0^{r}Bwxdx$

$E=B\omega [\frac{x^2}{2}{]}_2^r$

$=\frac{1}{2}B\omega r^2$

So,

$E=\frac{}{}0.4\times 10\times 25\times {10}^{-1}$

$=5\times 5\times {10}^{-3}V$

$i=\frac{E}{R}=\frac{5\times {10}^{-3}}{10}$

$i=0.5\times {10}^{-3}A$

Using right hand rule, we can say that the current is flowing away from the centre.