Two charged spheres of radius \(R_1\) and \(R_2\) respectively are charged and joined by a wire. The ratio of electric field of the spheres is ________.

A \(\frac{ R _2}{ R _1}\)
B \(\frac{R_1}{R_2}\)
C \(\frac{R_2{ }^2}{R_1{ }^2}\)
D \(\frac{R_1{ }^2}{R_2{ }^2}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{ R _2}{ R _1}\)

Step-by-step Solution

Detailed explanation

(A)
Two charged conducting sphere connected to each other by a wire so, potential of both sphere will be equal.
\(\therefore \quad V _1= V _2\)
\(\begin{aligned} \frac{K Q_1}{R_1} & =\frac{K Q_2}{R_2} \\ \frac{K Q_1}{R_1^2} \cdot R_1 & =\frac{K Q_2}{R_2^2} \cdot R_1 \\ E_1 R_1 & =E_2 R_2 \\ \frac{E_1}{E_2} & =\frac{R_2}{R_1}\end{aligned}\)

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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