10,000 electrons are passing per minute through a tube of radius 1 cm. the resulting current is:

Options

A. `42.5`
B. `40`
C. `43.46`
D. None of these

Explanation

To find the resulting current when 10,000 electrons are passing through a tube per minute, we can follow these steps:

### Step 1: Understand the relationship between current, charge, and time
Current (I) is defined as the rate of flow of charge. Mathematically, it can be expressed as:
\[ I = \frac{\Delta Q}{T} \]
where \( \Delta Q \) is the total charge flowing and \( T \) is the time in seconds.

### Step 2: Calculate the total charge (\( \Delta Q \))
The total charge can be calculated using the formula:
\[ \Delta Q = n \times e \]
where:
- \( n \) is the number of electrons (10,000 in this case),
- \( e \) is the charge of one electron, which is approximately \( 1.6 \times 10^{-19} \) coulombs.

### Step 3: Convert time from minutes to seconds
Since the electrons are passing through the tube per minute, we need to convert this time into seconds:
\[ T = 1 \text{ minute} = 60 \text{ seconds} \]

### Step 4: Substitute values into the charge formula
Now, substituting the values into the charge formula:
\[ \Delta Q = 10,000 \times 1.6 \times 10^{-19} \]

### Step 5: Calculate the total charge
Calculating \( \Delta Q \):
\[ \Delta Q = 10,000 \times 1.6 \times 10^{-19} = 1.6 \times 10^{-15} \text{ coulombs} \]

### Step 6: Substitute into the current formula
Now we can substitute \( \Delta Q \) and \( T \) back into the current formula:
\[ I = \frac{1.6 \times 10^{-15}}{60} \]

### Step 7: Calculate the current
Calculating the current:
\[ I = \frac{1.6 \times 10^{-15}}{60} = 2.67 \times 10^{-17} \text{ amperes} \]

### Final Answer
The resulting current is approximately:
\[ I \approx 2.67 \times 10^{-17} \text{ A} \]

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