TS EAMCET · Physics · Current Electricity

A particle of mass $2 \times 10^{- 6} kg$ with a charge $5 \times 10^{- 6} C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} M^{- 2}$ and $g = 10 m s^{- 2}$ )

A $35.4 \times 10^{- 12} C m^{- 2}$
B $23.6 \times 10^{- 12} C m^{- 2}$
C $53.1 \times 10^{- 12} C m^{- 2}$
D $17.7 \times 10^{- 12} C m^{- 2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $35.4 \times 10^{- 12} C m^{- 2}$

Step-by-step Solution

Detailed explanation

Given: Mass of the particle m=2×10-6 kg, charge on the particle q=5×10-6 C. Electric field due to conducting surface is given as E=σε0, where σ is the charge density and ε0 is the permittivity of free space. The force exerted by the…

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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A particle of mass 2×10-6 kg with a charge 5×10-6 C is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume ϵ0=8.85×10-12 C2 N-1M-2 and g=10 m s-2)

Step-by-step Solution

A particle of mass $2 \times 10^{- 6} kg$ with a charge $5 \times 10^{- 6} C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} M^{- 2}$ and $g = 10 m s^{- 2}$ )