A uniformly charged sphere carries a total charge of `2 pi xx10^(-12)` C. Its radius is 5 cm and is placed in vacuum. Determine its surface charge density.

Answer

To determine the surface charge density of a uniformly charged sphere, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Total charge, \( Q = 2\pi \times 10^{-12} \, \text{C} \)
- Radius of the sphere, \( r = 5 \, \text{cm} = 5 \times 10^{-2} \, \text{m} \)

2. **Formula for Surface Charge Density:**
The surface charge density \( \sigma \) is given by the formula:
\[ \sigma = \frac{Q}{A} \]
where \( A \) is the surface area of the sphere.

3. **Calculate the Surface Area of the Sphere:**
The surface area \( A \) of a sphere is calculated using the formula:
\[ A = 4\pi r^2 \]
Substituting the radius:
\[ A = 4\pi (5 \times 10^{-2})^2 \]
\[ A = 4\pi (25 \times 10^{-4}) = 100\pi \times 10^{-4} \, \text{m}^2 \]

4. **Substituting Values into the Surface Charge Density Formula:**
Now substitute \( Q \) and \( A \) into the surface charge density formula:
\[ \sigma = \frac{2\pi \times 10^{-12}}{100\pi \times 10^{-4}} \]

5. **Simplifying the Expression:**
The \( \pi \) cancels out:
\[ \sigma = \frac{2 \times 10^{-12}}{100 \times 10^{-4}} = \frac{2 \times 10^{-12}}{10^{-2}} \times \frac{1}{100} \]
\[ \sigma = \frac{2 \times 10^{-12 + 2}}{100} = \frac{2 \times 10^{-10}}{100} = 2 \times 10^{-10} \times 10^{-2} = 2 \times 10^{-12} \, \text{C/m}^2 \]

6. **Final Calculation:**
\[ \sigma = 2 \times 10^{-12} \, \text{C/m}^2 \]

### Final Answer:
The surface charge density \( \sigma \) of the uniformly charged sphere is:
\[ \sigma = 2 \times 10^{-12} \, \text{C/m}^2 \]