Q 12-02-036JEE MainJEE Main 2026 (6 Apr, Shift 1)Medium
A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$ N/C. The work done in moving the charge is ______ J.
Numerical value type. Enter your answer.
Answer: 186
Work done by the field: $W = q\displaystyle\int \vec{E} \cdot d\vec{l}$. Each component depends only on its own coordinate, so
$$\int_0^5 2x\,dx + \int_{-2}^{1} 3y^2\,dy + \int_{-5}^{2} 4\,dz = 25 + (1 + 8) + 28 = 62\ \text{V}$$
$W = 3 \times 62 = 186$ J.
Solution by Sreeraj P, M.Sc Physics