A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E = 2xi + 3y²j + 4k N/C. The work done in moving the charge is ______ J. Numerical answer type. Work it out, then open the answer.

Answer: 186. Work by the field: W = q∫ E· dl = q[∫ 2x dx + ∫ 3y² dy + ∫ 4 dz] ∫₀⁵ 2x dx = 25, ∫-2¹ 3y² dy = 1 - (-8) = 9, ∫-5² 4 dz = 28 W = 3(25 + 9 + 28) = 186 J

A three coulomb charge moves from the point (0, -2, -5) to the point… | JEE Main 2026 (6 Apr, Shift 1)

Q16JEE Main 2026 · 6 APR · SHIFT 1Medium

Electrostatic Potential Energy

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\text{ N/C}$ . The work done in moving the charge is ______ J.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 186

Work by the field: $W = q\int \vec{E}\cdot d\vec{l} = q\left[\int 2x\,dx + \int 3y^2\,dy + \int 4\,dz\right]$
$\int_0^5 2x\,dx = 25$ , $\int_{-2}^{1} 3y^2\,dy = 1 - (-8) = 9$ , $\int_{-5}^{2} 4\,dz = 28$
$W = 3(25 + 9 + 28) = 186$ J

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