If a charge q is moving in a circle of radius r with speed v, then the equivalent current will be :

Options

A. `(qv)/(2pir)`
B. `(qr)/(2piv)`
C. `(qr)/(2pi)`
D. `(qv)/(2pir^(2))`

Explanation

To find the equivalent current when a charge \( q \) is moving in a circle of radius \( r \) with speed \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Current**:
Current (\( I \)) is defined as the amount of charge (\( Q \)) flowing through a point in a circuit per unit time (\( t \)). Mathematically, it can be expressed as:
\[ I = \frac{Q}{t} \]

2. **Determine the Distance Traveled**:
When a charge \( q \) moves in a circle, it travels a distance equal to the circumference of the circle. The circumference \( C \) of a circle with radius \( r \) is given by:
\[ C = 2\pi r \]

3. **Calculate the Time Taken**:
The time (\( t \)) taken to complete one full circle can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{C}{v} = \frac{2\pi r}{v} \]

4. **Substituting into the Current Formula**:
Now, substituting the expression for time into the current formula:
\[ I = \frac{Q}{t} = \frac{Q}{\frac{2\pi r}{v}} = \frac{Q \cdot v}{2\pi r} \]

5. **Final Expression for Equivalent Current**:
Thus, the equivalent current \( I \) when a charge \( q \) is moving in a circle of radius \( r \) with speed \( v \) is:
\[ I = \frac{q \cdot v}{2\pi r} \]

### Conclusion:
The equivalent current is given by the formula:
\[ I = \frac{q \cdot v}{2\pi r} \]