Find the work done by an external agent in slowly shifting a charge q=1 μ C in the electric field vecE=103 hati V / m from the point P(1,2) m to Q(3,4) m.

Question

Find the work done by an external agent in slowly shifting a charge q=1 μ C in the electric field vecE=103 hati V / m from the point P(1,2) m to Q(3,4) m. (A) 2 × 10-3 J (B) 4 × 10-3 J (C) -2 × 10-3 J (D) -4 × 10-3 J

Tardigrade Admin · Accepted Answer

The work done against the electric field is W =-q ∫(E hati) ⋅(d x hati+d y hatj) =-q ∫ limitsx1x2 E d x =-q E(x2-x1) =-(10-6)(103 V / m )(3-1) =-2 × 10-3 J

Q. Find the work done by an external agent in slowly shifting a charge $q = 1 μ C$ in the electric field $E = 1 0^{3} \hat{i} V / m$ from the point $P (1, 2) m$ to $Q (3, 4) m$ .

$2 \times 1 0^{- 3} J$

$4 \times 1 0^{- 3} J$

$- 2 \times 1 0^{- 3} J$

$- 4 \times 1 0^{- 3} J$

The work done against the electric field is
$W = - q \int (E \hat{i}) \cdot (d x \hat{i} + d y \hat{j})$
$= - q x_{1} \int x_{2} E d x$
$= - qE (x_{2} - x_{1})$
$= - (1 0^{- 6}) (1 0^{3} V / m) (3 - 1)$
$= - 2 \times 1 0^{- 3} J$

Q. Find the work done by an external agent in slowly shifting a charge q=1μC in the electric field E=103i^V/m from the point P(1,2)m to Q(3,4)m.

2×10−3J

4×10−3J

−2×10−3J

−4×10−3J