AP EAMCET · PHYSICS · Electrostatics

Six point charges each of the magnitude \(Q\) are placed at the vertices of a regular hexagon of side \(a\) as shown in the figure. Electric field intensity on the line passing through the centre \(O\) and perpendicular to the plane of the figure at a large distance \(x(\gg > a)\) from \(O\) is
\(\left(\text {Let, } \frac{1}{4 \pi \in_0}=k\right)\)

A \(k \times \frac{4 Q a}{x^3}\)
B \(k \times \frac{2 Q a}{x^3}\)
C \(k \times \frac{8 Q a}{x^3}\)
D 0

Verified Solution

Answer & Solution

Correct Answer

(A) \(k \times \frac{4 Q a}{x^3}\)

Step-by-step Solution

Detailed explanation

According to the question, Let \(O K=x\) due to \(A B\), force at the point \(K\) is only along \(A B\) \(\text {i.e., } F_K=\frac{2 k Q a}{\left(a^2+x^2\right)^{\frac{3}{2}}}\) \(\therefore\) There are three such \(F_K^{\prime} s\) so the net resultant of these three,…

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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