An electron of charge 'e' is revolving in a circular orbit of radius r around a nucleus with speed v. The equivalent current is

Options

A. `2e pi r v`
B. e vr
C. `(ev)/(2 pi r)`
D. zero

Explanation

To find the equivalent current due to an electron revolving in a circular orbit around a nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the charge of the electron (e)**: The charge of an electron is a fundamental constant, denoted as 'e'.

2. **Determine the time period (T) for one complete revolution**:
- The electron travels in a circular path with a radius 'r'.
- The distance traveled in one complete revolution is the circumference of the circle, which is given by \(2\pi r\).
- The speed of the electron is given as 'v'.
- The time period (T) for one complete revolution can be calculated using the formula:
\[ T = \frac{\text{Distance}}{\text{Speed}} = \frac{2\pi r}{v} \]

3. **Calculate the equivalent current (I)**:
- Current is defined as the charge flowing per unit time. For one electron, the charge is 'e'.
- The equivalent current (I) can be expressed as:
\[ I = \frac{Q}{T} = \frac{e}{T} \]
- Substituting the expression for T from step 2:
\[ I = \frac{e}{\frac{2\pi r}{v}} = \frac{e \cdot v}{2\pi r} \]

4. **Final expression for the current**:
- Thus, the equivalent current due to the electron revolving in a circular orbit is:
\[ I = \frac{e \cdot v}{2\pi r} \]