Question

Find the work done by an external agent in slowly shifting a charge $q=1\, \mu C$ in the electric field $\vec{E}=10^{3} \hat{i} V / m$ from the point $P(1,2) m$ to $Q(3,4) m$.

• A. $2 \times 10^{-3} J$
• B. $4 \times 10^{-3} J$
• C. $-2 \times 10^{-3} J$
• D. $-4 \times 10^{-3} J$

Answer 1

Answer: (C)

The work done against the electric field is
$W =-q \int(E \hat{i}) \cdot(d x \hat{i}+d y \hat{j})$
$=-q \int\limits_{x_{1}}^{x_{2}} E d x$
$=-q E\left(x_{2}-x_{1}\right)$
$=-\left(10^{-6}\right)\left(10^{3} V / m \right)(3-1)$
$=-2 \times 10^{-3} J$