AP EAMCET · PHYSICS · Electrostatics

Four positive point charges \(+q\) are kept at the four corners of a square of side \(l\). The net electric field at the mid-point of any one side of the square is
\[
\left(\text { Take, } \frac{1}{4 \pi \varepsilon_0}=k\right)
\]

A \(\frac{4 k q}{1^2}\)
B \(\frac{16 k q}{5 \sqrt{5} l^2}\)
C \(\frac{8 k q}{\sqrt{5} /^2}\)
D \(\frac{k q}{l^2}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{16 k q}{5 \sqrt{5} l^2}\)

Step-by-step Solution

Detailed explanation

The force at midpoint of any side of a square let's say at point \(P\) which is midpoint of side \(A B\) is due to charges at corners \(A, B, C\) and \(D\) \[ F_P=F_{A P}+F_{B P}+F_{C P}+F_{D P} \]…

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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Four positive point charges \(+q\) are kept at the four corners of a square of side \(l\). The net electric field at the mid-point of any one side of the square is\[\left(\text { Take, } \frac{1}{4 \pi \varepsilon_0}=k\right)\]

Step-by-step Solution

Four positive point charges \(+q\) are kept at the four corners of a square of side \(l\). The net electric field at the mid-point of any one side of the square is
\[
\left(\text { Take, } \frac{1}{4 \pi \varepsilon_0}=k\right)
\]