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Physics · Electric Charges and Fields
हिन्दीA spherical metal body \( A \), initially neutral, gains protons from an ion beam at a steady rate of \( n_1 = 5 \times 10^{11} \text{ protons/second} \) while losing electrons at a steady rate of \( n_2 = 3 \times 10^{11} \text{ electrons/second} \). The time required for body \( A \) to accumulate a net positive charge of \( 1.28\,\mu\text{C} \) is:
Correct answer · Option 3
\( 10\text{ s} \)
Explanation
Gaining protons adds \( +e n_1 \) charge/sec and losing electrons adds \( +e n_2 \) charge/sec. Net rate of charging \( \frac{dq}{dt} = e(n_1 + n_2) = (1.6 \times 10^{-19}) \times (8 \times 10^{11}) = 1.28 \times 10^{-7}\text{ C/s} \). Time \( t = \frac{1.28 \times 10^{-6}\text{ C}}{1.28 \times 10^{-7}\text{ C/s}} = 10\text{ s} \).
