TS EAMCET · Physics · Electrostatics

A conducting sphere \(S_1\) of radius \(r_1\) is connected by a conducting wire to another conducting sphere \(S_2\) of radius \(r_2\), where \(r_1=3 \mathrm{~cm}\) and \(r_2=2\) \(\mathrm{cm}\). Before they are connected, \(s_1\) carries charge of 10 units. The electric potential at the point which is at a distance \(4 \mathrm{~cm}\) from the centre of \(S_1\) and a distance \(3 \mathrm{~cm}\) from the centre of \(S_2\) is

A \(\frac{1}{4 \pi \varepsilon_0} \frac{17}{6}\)
B \(\frac{1}{4 \pi \varepsilon_0} \frac{3}{2}\)
C \(\frac{1}{4 \pi \varepsilon_0} \frac{1}{6}\)
D \(\frac{1}{4 \pi \varepsilon_0} \frac{17}{12}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{4 \pi \varepsilon_0} \frac{17}{6}\)

Step-by-step Solution

Detailed explanation

When spheres are connected, charges are redistributed such that potential on their surfaces are same. So, we have \( \begin{aligned} q_1+q_2 & =10 \\ \frac{k q_1}{r_1} & =\frac{k q_2}{r_2} \Rightarrow \frac{q_1}{3}=\frac{q_2}{2} \end{aligned} \) and…

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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