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 midpoint of any one side of the square is $($ take $\frac{1}{4 π \in_{0}} = k$ )

A $\frac{4 k q}{l^{2}}$
B $\frac{16 k q}{5 \sqrt{5} l^{2}}$
C $\frac{8 k q}{\sqrt{5} l^{2}}$
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 electric field of EC & ED are equal and opposite so they cancel out each other, now net electric field at the midpoint of one side is, 2EAcosθ because EA=EB, so, Enet=2×k×ql2+l22cosθEnet=2×k×ql2+l222×ll2+l22Enet=16 kq55l2

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 midpoint of any one side of the square is (take 14π∈0=k)

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 midpoint of any one side of the square is $($ take $\frac{1}{4 π \in_{0}} = k$ )