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
Concept. Work by the field $W=q\int\vec E\cdot d\vec l$. Each component integrates separately (this field is conservative, so the path does not matter).
Step 1. Integrals. $\int_0^5 2x\,dx=25$; $\int_{-2}^{1}3y^2dy=1-(-8)=9$; $\int_{-5}^{2}4\,dz=28$.
Step 2. Work. $3\times(25+9+28)=186$ J.
Answer. $186$.
Solution by Sreeraj P, M.Sc Physics
