Question

The surface density of charge on the surface of a charged conductor in air is \( 0.885 \, \mu C/m^2 \). The outward force per unit area of charged conductor is:

• A. \( 5 \times 10^{-3} \, \text{N/m}^2 \)
• B. \( 4.425 \times 10^{-2} \, \text{N/m}^2 \)
• C. \( 5 \times 10^{-2} \, \text{N/m}^2 \)
• D. \( 8.85 \times 10^{-2} \, \text{N/m}^2 \)

Hint:

The outward force per unit area is related to the surface charge density by the formula \( F/A = \frac{\sigma^2}{2 \epsilon_0} \).

Answer 1

The Correct Option is B

Step 1: Formula for Surface Charge.
The outward force per unit area \( F/A \) on a charged conductor is given by: \[ F/A = \frac{\sigma^2}{2 \epsilon_0} \] where \( \sigma \) is the surface charge density and \( \epsilon_0 \) is the permittivity of free space. Substituting the given values: \[ F/A = \frac{(0.885 \times 10^{-6})^2}{2 \times 8.85 \times 10^{-12}} = 4.425 \times 10^{-2} \, \text{N/m}^2 \] Step 2: Final Answer.
Thus, the outward force per unit area is \( 4.425 \times 10^{-2} \, \text{N/m}^2 \).