Question

The insulation property of air breaks down at \( 3 \times 10^6 \, \text{V/m} \). The maximum charge that can be given to a sphere of diameter 5 m is nearly:

• A. \( 2 \times 10^{-10} \, \text{C} \)
• B. \( 2 \times 10^{-3} \, \text{C} \)
• C. \( 2 \times 10^{-6} \, \text{C} \)
• D. \( 2 \times 10^{-5} \, \text{C} \)

Hint:

The maximum charge that can be stored on a sphere is determined by the dielectric breakdown strength of the surrounding medium.

Answer 1

The Correct Option is A

Step 1: Use the formula for capacitance.
The capacitance of a sphere is given by: \[ C = 4 \pi \epsilon_0 r \] where \( r \) is the radius of the sphere. The charge \( Q \) is related to the voltage \( V \) and capacitance \( C \) by: \[ Q = C V \]
Step 2: Calculate the maximum charge.
Substituting the given values, we find the maximum charge that can be given to the sphere.
Final Answer: \[ \boxed{2 \times 10^{-10} \, \text{C}} \]