If `10^(6)` electrons/s are flowing through an area of cross section of `10^(-4) m^(2)` then the current will be:-

Options

A. `1.6xx10^(-7)A`
B. `1.6xx10^(-13)A`
C. ` 1xx10^(-6)A`
D. `1xx1^(2)A`

Answer

To find the current flowing through a cross-sectional area when a certain number of electrons are passing through, we can use the relationship between charge, current, and time. Here’s how to solve the problem step by step:

### Step 1: Understand the relationship between current, charge, and time
The formula for current (I) is given by:
\[ I = \frac{Q}{T} \]
where:
- \( I \) is the current in amperes (A),
- \( Q \) is the total charge in coulombs (C),
- \( T \) is the time in seconds (s).

### Step 2: Calculate the total charge flowing per second
We know that the charge of a single electron is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]
Given that \( 10^6 \) electrons are flowing per second, the total charge \( Q \) can be calculated as:
\[ Q = n \cdot e \]
where \( n \) is the number of electrons.

Substituting the values:
\[ Q = 10^6 \cdot (1.6 \times 10^{-19}) \]

### Step 3: Calculate the total charge
Now, we can calculate \( Q \):
\[ Q = 10^6 \cdot 1.6 \times 10^{-19} = 1.6 \times 10^{-13} \, \text{C} \]

### Step 4: Substitute the charge into the current formula
Since the time \( T \) is 1 second (as we are calculating the current per second), we can substitute \( Q \) into the current formula:
\[ I = \frac{Q}{T} = \frac{1.6 \times 10^{-13}}{1} \]

### Step 5: Final calculation of current
Thus, the current \( I \) is:
\[ I = 1.6 \times 10^{-13} \, \text{A} \]

### Final Answer:
The current flowing through the area is \( 1.6 \times 10^{-13} \, \text{A} \).

---