Current from a Rotating Charged Ring

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Electric Circuits Beginner Electric Current

Source: High school physics (Chinese)

Problem

On a dielectric ring of radius $R$, each unit length carries an electric charge $\lambda$. The ring rotates with angular velocity $\omega$ in its own plane about its center, forming a circular current.

Find the current intensity of this circular current.
$I = \lambda R \omega$

The total charge on the ring is:

$$Q = 2\pi R \lambda$$

The ring completes one revolution in period:

$$T = \frac{2\pi}{\omega}$$

The current equals charge passing a fixed cross-section per unit time, which is the total charge divided by the period:

$$I = \frac{Q}{T} = \frac{2\pi R \lambda}{2\pi / \omega} = \lambda R \omega$$