द्रव्यमान ' \(m\) ' का एक धनात्मक आवेश \(' q '+x\) अक्ष पर गतिशील है। हम एक एकसमान चुम्बकीय क्षेत्र \(B\) समय \(\Delta t\) के लिए लगाना चाहते हैं जिससे कि आवेश की दिशा \(d\) दूरी पर \(y\)-अक्ष को काटते हुए प्रतिलोमित हो जाए, तब

A \(B\, = \,\frac{{mv}}{{qd}}\) एवं \(\Delta t\, = \,\frac{{\pi d}}{v}\)
B \(B\, = \,\frac{{mv}}{{2qd}}\) एवं \(\Delta t\, = \,\frac{{\pi d}}{2v}\)
C \(B\, = \,\frac{{2mv}}{{qd}}\) एवं \(\Delta t\, = \,\frac{{\pi d}}{2v}\)
D \(B\, = \,\frac{{2mv}}{{qd}}\) एवं \(\Delta t\, = \,\frac{{\pi d}}{v}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(B\, = \,\frac{{2mv}}{{qd}}\) एवं \(\Delta t\, = \,\frac{{\pi d}}{2v}\)

Step-by-step Solution

Detailed explanation

The applied magnetic field provides the required centripetal force to the charge particle, so it can move in circular path of radius \(\frac{d}{2}\) \(\therefore \mathrm{Bqv}=\frac{\mathrm{mv}^{2}}{\mathrm{d} / 2}\) or, \(B = \frac{{2{\text{mv}}}}{{{\text{qd}}}}\) Time interval…

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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