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

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Electrostatics

A three coulomb charge moves from the point

(0, - 2, - 5)

to the point

(5, 1, 2)

in an electric field expressed as

E = 2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k} N / C

. The work done in moving the charge is

____

Answer: 186

The work done by the field is

W = q \int E \cdot d r = q [\int_{0}^{5} 2 x d x + \int_{- 2}^{1} 3 y^{2} d y + \int_{- 5}^{2} 4 d z]

. Evaluating,

\int_{0}^{5} 2 x d x = 25

\int_{- 2}^{1} 3 y^{2} d y = [y^{3}]_{- 2}^{1} = 1 - (- 8) = 9

, and

\int_{- 5}^{2} 4 d z = 4 \times 7 = 28

, summing to

62

. With

q = 3

C, the work done is

3 \times 62 = 186

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Integer answer