Question

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).

Answer 1

In Fig, a charge `q = 8 mC = 8xx10^(-3)C` is located at the origin O, charge to be carried is
`q_(0) = -2xx10^(-9)C`, from p to Q
Where `OP = r_(p) = 3 cm = 3xx10^(-2) m`
and `OQ = r_(Q) = 4cm = 4xx10^(-2) m`
As electrostatic forces are conervative forces, work done is independent of the path. Therefore, there si no relevance of point R.
`W_(PQ) = q_(0) (V_(Q) - V_(P))`
`W_(PQ) = (qq_(0))/(4pi in_(0)) ((1)/(r_(Q)) - (1)/(r_(p)))`
`= 9xx10^(9)xx8xx10^(-3) (-2xx10^(-9)) [(1)/(4xx10^(-2)) - (1)/(3xx10^(-2))]`
`= -144xx10^(-3)xx10^(2) (- (1)/(12)) = 1.2 joul e`