આકૃતિમાં દર્શાવ્યા મુજબ \(Q\) વિજભાર ધરાવતાં \(L\) લંબાઈ અને એક સમાન વીજભારિત પાતળા તારનાં લંબ દ્વિભાજક પર આવેલ બિંદુ \(P\) પરનું વિદ્યૂતક્ષેત્ર શોધો. બિંદુ \(P\) નું સળિયાનાં કેન્દ્ર થી અંતર \(a=\frac{\sqrt{3}}{2} L\) છે.

A \(\frac{\sqrt{3} Q }{4 \pi \varepsilon_{0} L ^{2}}\)
B \(\frac{ Q }{3 \pi \varepsilon_{0} L ^{2}}\)
C \(\frac{Q}{2 \sqrt{3} \pi \varepsilon_{0} L ^{2}}\)
D \(\frac{ Q }{4 \pi \varepsilon_{0} L ^{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{Q}{2 \sqrt{3} \pi \varepsilon_{0} L ^{2}}\)

Step-by-step Solution

Detailed explanation

\(E =\frac{ k \lambda}{ a }\left(\sin \theta_{1}+\sin \theta_{2}\right)\) \(E =\frac{1}{4 \pi \varepsilon_{0}} \times \frac{ Q }{ L } \times \frac{1}{\left(\frac{\sqrt{3 L }}{2}\right)} \times(2 \sin \theta)\)…

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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