Question

A metal cube of side 5 cm is charged with 6 μC. The surface charge density on the cube is

• A. \(0.125 \times 10^{-3} \, \text{C} \, \text{m}^{-2}\)
• B. \(0.25 \times 10^{-3} \, \text{C} \, \text{m}^{-2}\)
• C. \(4 \times 10^{-3} \, \text{C} \, \text{m}^{-2}\)
• D. \(0.4 \times 10^{-3} \, \text{C} \, \text{m}^{-2}\)

Answer 1

The Correct Option is D

Surface Charge Density on a Cube

1. Surface charge density $\sigma$ 

$$ \sigma = \frac{\text{Charge }(Q)}{\text{Surface Area }(A)} $$

2. Given data

$$ \text{Side of cube} = 5 \, \text{cm} = 0.05 \, \text{m} $$ $$ Q = 6 \, \mu\text{C} = 6 \times 10^{-6} \, \text{C} $$

3. Total surface area of cube

A cube has 6 faces:

$$ A = 6 \times (\text{side})^2 = 6 \times (0.05)^2 $$

$$ A = 6 \times 0.0025 = 0.015 \, \text{m}^2 $$

4. Calculate $\sigma$

$$ \sigma = \frac{6 \times 10^{-6} \, \text{C}}{0.015 \, \text{m}^2} $$

$$ \sigma = 4.0 \times 10^{-4} \, \text{C/m}^2 = 0.4 \times 10^{-3} \, \text{C m}^{-2} $$

Surface charge density $\sigma = 4.0 \times 10^{-4} \, \text{C/m}^2$

or $0.4 \, \text{mC/m}^2$