A metal cube of length 0.1 is charged by `12 mu C`. Calculate its surface charge density.

Answer

To calculate the surface charge density of a metal cube with a given charge, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Length of the cube (L) = 0.1 m
- Charge (Q) = 12 µC = 12 × 10^(-6) C

2. **Calculate the Surface Area of the Cube**:
The surface area (A) of a cube is given by the formula:
\[ A = 6 \times L^2 \]
Substituting the length of the cube:
\[ A = 6 \times (0.1)^2 = 6 \times 0.01 = 0.06 \, \text{m}^2 \]

3. **Use the Formula for Surface Charge Density**:
Surface charge density (σ) is defined as the charge per unit area:
\[ \sigma = \frac{Q}{A} \]
Substituting the values of charge and area:
\[ \sigma = \frac{12 \times 10^{-6}}{0.06} \]

4. **Perform the Calculation**:
\[ \sigma = \frac{12 \times 10^{-6}}{0.06} = 12 \times 10^{-6} \div 6 \times 10^{-2} \]
\[ \sigma = 2 \times 10^{-4} \, \text{C/m}^2 \]

5. **State the Final Answer**:
The surface charge density of the metal cube is:
\[ \sigma = 2 \times 10^{-4} \, \text{C/m}^2 \]

### Summary of the Solution:
- The surface charge density of the metal cube is \( \sigma = 2 \times 10^{-4} \, \text{C/m}^2 \).