MHT CET · Physics · Electrostatics
A uniformly charged conducting sphere of diameter 3.5 cm has a surface charge density of \(20 \mu \mathrm{C} \mathrm{m}^{-2}\). The total electric flux leaving the surface of the sphere is nearly
[permittivity of free space, \(\epsilon_0=8.85 \times 10^{-12} \mathrm{SI}\) unit]
- A \(7 \times 10^2 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}\)
- B \(7.0 \times 10^3 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}\) (or \(70 \times 10^2\))
- C \(8.7 \times 10^2 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}\)
- D \(8.7 \times 10^3 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}\)
Answer & Solution
Correct Answer
(D) \(8.7 \times 10^3 \mathrm{~N} \cdot \mathrm{~m}^2 / \mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(r = 3.5 \text{ cm} / 2 = 1.75 \times 10^{-2} \text{ m}\) \(\Phi_E = \frac{\sigma \cdot 4 \pi r^2}{\epsilon_0} = \frac{20 \times 10^{-6} \cdot 4 \pi (1.75 \times 10^{-2})^2}{8.85 \times 10^{-12}} \approx 8.7 \times 10^3 \text{ N m}^2 / \text{C}\)
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