A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of `-2 xx 10^(-9)C` from a point P(0,0,3 cm) to a point Q10,4 cm, 0) via a point R(0,6 cm, 9 cm).

Explanation

As electrostatic field is a conservative field hence work done in taking a small charge from point P to Q is independent of the path followed.
As q = 8 mC `= 8 xx 10^(-3) C, q_0 = -2 xx 10^(-9) C`
At point P, `r_1 = 3 cm = 0.03 m` and at point Q,`r_2 = 4 cm = 0.04 m`
`:.` Work done `W = q_0 (V_2 - V_1) = q_0 1/(4pi epsi_0) .q[1/r_2-1/r_1] = (q_0q)/(4pi epsi_0) [ 1/r_2 - 1/r_1]`
`:. W = 9 xx 10^9 xx (-2 xx 10^(-9))xx (8 xx 10^(-3)) [ 1/0.04 - 1/0.03] = 1.2 J`