જો \({q}_{{f}}\) એ કેપેસિટર પ્લેટો પરનો મુક્ત વિદ્યુતભાર અને \({q}_{{b}}\) એ કેપેસિટર વચ્ચે મૂકવામાં આવેલા ડાઇલેક્ટ્રિક અચળાંક \(k\) ના ડાઇલેક્ટ્રિક ચોચલા પરનો બાઉન્ડ ચાર્જ હોય, તો બાઉન્ડ ચાર્જ \(q_{b}\) ને કઈ રીતે દર્શાવાય?

A \({q}_{{b}}={q}_{{f}}\left(1-\frac{1}{{k}}\right)\)
B \({q}_{{b}}={q}_{{f}}\left(1-\frac{1}{\sqrt{{k}}}\right)\)
C \({q}_{{b}}={q}_{{f}}\left(1+\frac{1}{\sqrt{{k}}}\right)\)
D \({q}_{{b}}={q}_{{f}}\left(1+\frac{1}{{k}}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \({q}_{{b}}={q}_{{f}}\left(1-\frac{1}{{k}}\right)\)

Step-by-step Solution

Detailed explanation

When a dielectric is inserted in a capacitor Due to free charge \(\vec{E}=\vec{E}_{0}\) only After dielectric \(E^{\prime}=\frac{E_{0}}{k}\) \(q_{B}=q_{f}\left(1-\frac{1}{k}\right)\)

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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