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 Q (0, 4 cm, 0), via a point R (0, 6 cm, 9 cm)

Explanation

The work done for bringing charge from one point to other is path independent hence, work done from P to Q,
`W = q_(0) [ V_(Q)-V_(P)]`
` =q_(0)[(kq)/(r_(2))-(kq)/(r_(1))]`
`W = (kqq_(0))/(1) [(1)/(r_(2))-(1)/(r_(1))]`

Here K `= 9xx10^(9) Nm^(2) C^(-2)`
`q_(0)= -2xx10^(-9)C`
`q = 8 mC = 8xx10^(-3) C `
`r_(1)= 3 cm = 3xx10^(-2) m`
`r_(2) = 4 cm = 4xx10^(-2) m`
Putting these values in equation (1)
`W=(9xx10^(9)xx8xx10^(-3)xx(-2xx10^(-9)))/(1)[(100)/(4)-(100)/(3)]`
`= -144 xx10^(-3) [-(100)/(12)]`
`:. ` W = (14.4)/(12) = 1.2 ` J Point R has no relation with answer .