JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance

આકૃતિમાં દર્શાવ્યા મુજબ બે સમાંતર વાહક પ્લેટોની મદદથી મળતા વિદ્યુતક્ષેત્રમાં \(m\) દળ ધરાવતું, \(l\) લંબાઈ ધરાવતું અને \(+q\) વિદ્યુતભાર ધરાવતા એક સાદા લોલકને લટકાવેલ છે. તો સંતુલિત સ્થિતિમાં સાદા લોલકનું વિચલન ......... થશે?

A \(\tan ^{-1}\left[\frac{{q}}{{mg}} \times \frac{{C}_{2}\left({V}_{2}-{V}_{1}\right)}{\left({C}_{1}+{C}_{2}\right)({d}-{t})}\right]\)
B \(\tan ^{-1}\left[\frac{{q}}{{mg}} \times \frac{{C}_{1}\left({V}_{1}+{V}_{2}\right)}{\left({C}_{1}+{C}_{2}\right)({d}-{t})}\right]\)
C \(\tan ^{-1}\left[\frac{{q}}{m g} \times \frac{C_{1}\left(V_{2}-V_{1}\right)}{\left(C_{1}+C_{2}\right)(d-t)}\right]\)
D \(\tan ^{-1}\left[\frac{{q}}{{mg}} \times \frac{{C}_{2}\left({V}_{1}+{V}_{2}\right)}{\left({C}_{1}+{C}_{2}\right)({d}-{t})}\right]\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\tan ^{-1}\left[\frac{{q}}{{mg}} \times \frac{{C}_{2}\left({V}_{1}+{V}_{2}\right)}{\left({C}_{1}+{C}_{2}\right)({d}-{t})}\right]\)

Step-by-step Solution

Detailed explanation

Let \(E\) be electric field in air \(T \sin \theta=q E\) \(T \cos \theta=m g\) \(\tan \theta=\frac{q {E}}{m g}\) \({Q}=\left[\frac{{C}_{1} {C}_{2}}{{C}_{1}+{C}_{2}}\right]\left[{V}_{1}+{V}_{2}\right]\)…

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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