Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is

Options

A. `1.35xx10^(-7)J`
B. `2.7xx10^(-7)J`
C. `2.0xx10^(-7)J`
D. `12.1xx10^(-7)J`

Answer

A

Explanation

`A=+3nC = 3xx10^(-9)C`
`B=+1 nC = 1xx10^(-9)C`
Distance, `r_(1)=5 cm = 0.05 m = 5xx10^(-2)m`
Workdone `(W)=U_(B)-U_(A)`
`= (kq_(1)q_(2))/(r_(2))-(kq_(1)q_(2))/(r_(1))`
Here, `r_(2)=r_(1)-1`
`r_(2)=5-1=4 cm = 0.04 m = 4xx10^(-2)m`
`= kq_(1)q_(2)[(1)/(r_(2))-(1)/(r_(1))]`
`= 9xx10^(9)xx3xx10^(-9)xx1xx10^(-9)`
`= [(1)/(4xx10^(-2))-(1)/(5xx10^(-2))]`
`=(27xx10^(-9)xx1)/(5xx4xx10^(-2))`
`= (27)/(20)xx10^(-7)`
`= 1.35xx10^(-7)J`