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

Explanation

Charge `q_(O)` at origin `O=8" mC"=8xx10^(-3)C`
Charge `q_(p)` at point `p=-2xx10^(-9)C`
Distance `OP=r_(p)=3" cm"=0.03m`
Distance, `OQ=r_(Q)=4" cm "=0.04` m

Work done bringing the charge `q_(p)` from p to Q
`=qxx` Potential differnce between Q and P
`=-2xx10^(-9)((1)/(4piepsi_(0))*(q_(O))/(OQ)-(1)/(4piepsi_(0))*(q_(O))/(OP))`
`=-2xx10^(-9)((9xx10^(9)xx8xx10^(-3))/(0.04)-(9xx10^(9)xx8xx10^(-3))/(0.03))`
`=-2xx10^(-9)xx9xx10^(9)xx8xx10^(-3)((1)/(0.04)-(1)/(0.03))`
`=-18xx8xx10^(-3)(-(0.01)/(0.0012))=(18xx8xx10^(-3)xx0.01)/(0.0012)`
`=1.2` J
Thus, the work done in bringing the charge of `-2xx10^(-9)C` from P to Q is `1.2` J.