Question

Question 2.12: A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of −2 × 10 −9 C from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm).

Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-88

Answer 1

as you know that electric field is conservative field, so work done in moving a charge in electric field is independent of path chosen to move the charge in electric field and depends only on the electric potential difference between them.
e.g., $W_{PQ}=q_0[V_Q-V_P]$
$W_{PQ}=q_0\left[\begin{array}{c}\frac{1}{4\pi\epsilon_0}\frac{q}{r_{OQ}}-\frac{1}{4\pi\epsilon_0}\frac{q}{r_{OP}}\end{array}\right]$

$r_{OQ}$=4cm [ see figure]
$r_{OP}$=3cm [ see figure]
$W_{PQ}$ = qq₀/4πε₀ [1/4 - 1/3]
= 9 × 10⁹ × 8 × 10³ × (-2 × 10⁻⁹) × (-1/12)
= -1.2 J

Hence, Workdone = 1.2 J