An electron moves in a circular orbit of radius 10 cm with a constant speed of `4.0xx10^(6) ms^(-1)`. Determine the electric current at a point on the orbit.

Answer

To determine the electric current at a point on the orbit of an electron moving in a circular path, we can follow these steps:

### Step 1: Identify the given values
- Radius of the circular orbit, \( r = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Speed of the electron, \( v = 4.0 \times 10^6 \, \text{m/s} \)

### Step 2: Calculate the circumference of the circular orbit
The circumference \( C \) of the circular orbit can be calculated using the formula:
\[ C = 2 \pi r \]
Substituting the radius:
\[ C = 2 \pi (0.1) = 0.2 \pi \, \text{m} \approx 0.628 \, \text{m} \]

### Step 3: Calculate the time period \( T \)
The time period \( T \) is the time taken to complete one full circle. It can be calculated using the formula:
\[ T = \frac{C}{v} \]
Substituting the values:
\[ T = \frac{0.628}{4.0 \times 10^6} \approx 1.57 \times 10^{-7} \, \text{s} \]

### Step 4: Calculate the electric current \( I \)
The electric current \( I \) can be calculated using the formula:
\[ I = \frac{Q}{T} \]
Where \( Q \) is the charge of the electron. The charge of an electron \( Q = 1.6 \times 10^{-19} \, \text{C} \).

Substituting the values:
\[ I = \frac{1.6 \times 10^{-19}}{1.57 \times 10^{-7}} \approx 1.02 \times 10^{-12} \, \text{A} \]

### Final Answer
The electric current at a point on the orbit is approximately:
\[ I \approx 1.02 \times 10^{-12} \, \text{A} \]

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