A charge of 3 C is moved from point:

A(0, −2, −5)

to point:

B(5, 1, 2)

in an electric field:

E = 2x î + 3y² ĵ + 4k̂ N/C

Find the work done in moving the charge from A to B.

Work done by an electric field is:

W = q ∫ E · dr

Given:

E = 2x î + 3y² ĵ + 4k̂

and:

dr = dx î + dy ĵ + dz k̂

Therefore:

E · dr = 2x dx + 3y² dy + 4 dz

Integrating from point A to point B:

∫2x dx = x²

= 5² − 0²

= 25

∫3y² dy = y³

= 1³ − (−2)³

= 1 + 8

= 9

∫4 dz = 4(z₂ − z₁)

= 4(2 − (−5))

= 28

Total potential difference:

25 + 9 + 28 = 62

Since charge q = 3 C:

W = 3 × 62

= 186 J

Final Answer

186 J