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