GATE 2024 IN – Question 36
A circular wire of radius $a$ has current density $J=ks^2$, where $k$ is constant and $s$ is radial distance from the axis ($0\le s\le a$). Its total current is
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Correct answer: (A) $\pi ka^4/2$
Explanation
An annular area element is $dA=2\pi s\,ds$. Integrate the current density: $I=\int_0^a ks^2(2\pi s)\,ds=2\pi k[a^4/4]=\pi ka^4/2$.
Answer: **A**.