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. `2.0 xx 10^(-7)J`
B. `1.35 xx 10^(-7)J`
C. `2.7 xx 10^(-7)J`
D. `12.1 xx 10^(-7)J`

Answer

B

Explanation

Required work done =Change in potential energy of the system
`W=U_(f)-U_(i)=k(q_(1)q_(2))/(r_(f))-k(q_(1)q_(2))/(r_(i))=kq_(1)q_(2)[(1)/(r_(f))-(1)/(r_(i))]`
`:. W=(9 xx 10^(9))(3 xx 10^(-9) xx 1 xx 10^(-9)) xx [(1)/(4 xx 10^(-2))-(1)/(5 xx 10^(-2))]`
`= 27 xx 10^(-7) xx (0.05)=1.35 xx 10^(-7) J`