First slide

Electrostatic potential

Question

16. The work done in carrying a particle of a charge 2C from B (1m, 0, 1m) to A(0.8m, 0.6m, 1m) in a non-uniform electric field $E = (\hat{i} + x \hat{j} + \hat{k}) N / m$ along the straight line path from B to A is

Difficult

A

$- 0.96 J$
B

$+ 0.96 J$
C

Zero
D

$- 0.48 J$

Solution

$d W = - q \bar{E} \cdot d \bar{r}$
$\begin{array}{l} = - {qE}_{x} dx - q E_{y} dy - q E_{z} dz \\ = - 2 ydx - 2 xdy - 2 d z \\ = - 2 d (xy) - 2 dz \\ w = [- 2 xy - 2 z] \\ = [- 0 .8 \times 0 .6 \times 2 - 2] - 2 (- 1) = - 0 .965 . \end{array}$

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