A charge of 8 mC is located at the origin. Calculate the work done in taking a small charge of `-2xx10^(-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, 9cm).

Explanation

Work done in moving the charge from one point to another in an external field is independent of the path and depends only on the initial and final points, so mentioning point R in the question is of no use.

charge fixed at origin, `q=8xx10^(-3)C`
Charge to be moved, `q.=-2xx10^(-9)C`
From the figure we can find:
Distance of point P from origin, `r_(P)=3xx10^(-2)m`
Distance of point Q from origin, `r_(Q)=4xx10^(-2)m`

Work done can be calculated as
`W=q.(V_(Q)-V_(P))`
`W=(qq.)/(4pi epsilon_(0))[(1)/(r_(Q))-(1)/(r_(P))]`
`W=9xx10^(9)xx8xx10^(-3)xx(-2xx10^(-9))xx [(1)/(4xx10^(-2))-(1)/(3xx10^(-2))]`
`=1.2J`