A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as

Question

A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as $\vec{E} = 2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k} N / C .$ The work done in moving the charge is _______ J. [2026]

Smart Achievers · Accepted Answer

(186)

$Given: Charge = 3 C, \vec{E} = 2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k} N/C$

$Work done W = q \int_{A}^{B} \vec{E} \cdot d \vec{r}$

$= 3 \int_{(0, - 2, - 5)}^{(5, 1, 2)} (2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k})$

$= 3 [\int_{0}^{5} 2 x d x + \int_{- 2}^{1} 3 y^{2} d y + \int_{- 5}^{2} 4 d z]$

$= 3 [{[x^{2}]}_{0}^{5} + {[y^{3}]}_{- 2}^{1} + 4 {[z]}_{- 5}^{2}] = 186 J$

Solution

Q.
A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as $\vec{E} = 2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k} N / C .$ The work done in moving the charge is _______ J. [2026]

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Solution

Q. 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. [2026]

Ans. (186) Given: Charge=3 C, E→=2xi^+3y2j^+4k^ N/C Work done W=q∫ABE→·dr→ =3∫(0,-2,-5)(5,1,2)(2xi^+3y2j^+4k^)·(dxi^+dyj^+dzk^) =3[∫052x dx+∫-213y2 dy+∫-524 dz] =3[[x2]05+[y3]-21+4[z]-52]=186 J

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Q.
A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as $\vec{E} = 2 x \hat{i} + 3 y^{2} \hat{j} + 4 \hat{k} N / C .$ The work done in moving the charge is _______ J. [2026]