COMEDK · Physics · 17. Electrostatics

A uniformly charged conducting sphere of 0.2 m diameter has a surface charge density of \(70 \mu \mathrm{Cm}^{-2}\). The electric flux leaving the surface of the sphere is:

A \(9.9 \times 10^6 N C^{-1} m^2\)
B \(8.9 \times 10^6 N C^{-1} m^2\)
C \(8.9 \times 10^5 N C^{-1} m^2\)
D \(9.9 \times 10^5 N C^{-1} m^2\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(9.9 \times 10^5 N C^{-1} m^2\)

Step-by-step Solution

Detailed explanation

The diameter of the sphere is \(d = 0.2\) m, so the radius is \(r = 0.1\) m. The surface area of the sphere is \(A = 4 \pi r^2 = 4 \pi (0.1)^2 = 0.04 \pi\) m\(^2\). The total charge \(Q\) on the sphere is given by \(Q = \sigma A\), where \(\sigma = 70 \times 10^{-6}\) C…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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