AP EAMCET · PHYSICS · Electrostatics

Two small spheres each having equal positive charge \(Q\) (Coulomb) on each are suspended by two insulating strings of equal length \(L\) (metre) from a rigid hook (shown in figure). The whole set up is taken into satellite where there is no gravity. The two balls are now held by electrostatic forces in horizontal position, the tension in each string is then

A \(\frac{Q^2}{16 \pi \varepsilon_0 L^2}\)
B \(\frac{Q^2}{8 \pi \varepsilon_0 L^2}\)
C \(\frac{Q^2}{4 \pi \varepsilon_0 L^2}\)
D \(\frac{Q^2}{2 \pi \varepsilon_0 L^2}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{Q^2}{16 \pi \varepsilon_0 L^2}\)

Step-by-step Solution

Detailed explanation

In this case, tension will be equal to force The tension in each string \(\begin{aligned} T & =F \\ & =\frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{(2 L)^2} \\ & =\frac{Q^2}{16 \pi \varepsilon_0 L^2}\end{aligned}\)

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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