CUET · PHYSICS · PYQ PAPER 2023

A spherical metallic conductor of radius \(6 . 0 ~ c m\) is held in air. The maximum charge it can hold if
dielectric strength of air is \(20 kV / cm\) will be :
\(\left(\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 N m^2 C^{-2}\right)\)

A \(0.8 \mu C\)
B \(8.0 \mu C\)
C \(80 \mu C\)
D \(8 \mu C\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(0.8 \mu C\)

Step-by-step Solution

Detailed explanation

\(R = 6.0 \text{ cm} = 0.06 \text{ m}\) \(E_{max} = 20 \text{ kV/cm} = 20 \times 10^3 \text{ V} / (10^{-2} \text{ m}) = 20 \times 10^5 \text{ V/m}\) \(Q_{max} = E_{max} R^2 (4 \pi \epsilon_0)\) \(Q_{max} = \frac{E_{max} R^2}{\left(\frac{1}{4 \pi \epsilon_0}\right)}\)…

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 spherical metallic conductor of radius \(6 . 0 ~ c m\) is held in air. The maximum charge it can hold ifdielectric strength of air is \(20 kV / cm\) will be :\(\left(\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 N m^2 C^{-2}\right)\)

Step-by-step Solution

A spherical metallic conductor of radius \(6 . 0 ~ c m\) is held in air. The maximum charge it can hold if
dielectric strength of air is \(20 kV / cm\) will be :
\(\left(\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9 N m^2 C^{-2}\right)\)