A cycle wheel of radius $0.5 ext{ m}$ is rotated with a constant angular velocity of $10 ext{ rad/s}$ in a

Question

A cycle wheel of radius $0.5 	ext{ m}$ is rotated with a constant angular velocity of $10 	ext{ rad/s}$ in a region of a magnetic field of $0.1 	ext{ T}$ which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is:

Accepted Answer

The induced electromotive force (emf) $\varepsilon$ generated between the center (axle) and the rim of a rotating conductor (like a wheel or rod) in a uniform magnetic field perpendicular to the plane of rotation is given by the formula :
$$ \varepsilon = \frac{1}{2} B \omega R^2 $$
Where:
*   $B$ is the magnetic field strength ($0.1 	ext{ T}$).
*   $\omega$ is the angular velocity ($10 	ext{ rad/s}$).
*   $R$ is the radius or length of the conductor ($0.5 	ext{ m}$).

**Calculation:**
$$ \varepsilon = \frac{1}{2} 	imes 0.1 	imes 10 	imes (0.5)^2 $$
$$ \varepsilon = 0.5 	imes 1 	imes 0.25 $$
$$ \varepsilon = 0.125 	ext{ V} $$

*Note: Even if the wheel has multiple spokes, they are connected in parallel between the center and the rim, so the net emf remains the same as that of a single spoke .*

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