An electric dipole consists of charges `pm 2.0 xx 10^(8) C` separated by a distance of `2.0 xx 10^(-3)` m. It is placed near a long ilne charge of linear charge density `4.0 xx 10^(-4) C m^(-1)` as shown in figure (30-W4), Such thet the negative charge is at a distance of `2.0 cm from the line charge. Find the force acting on the dipole.

Explanation

The electric field at a distance r from the line charge of linear density `lembda` is given by
`E= lambda/2pi epsilon_0 r.
Hence. The field at the negative charge is
`E_1= (4.0 xx 10_(-4) C M^(-1) (2 xx 9 xx 10^9 N m^2 C^(-2)/0.02m`
`=3.6 xx 10^8 N C^(-1)`.
The force on the negative charge is
`F_1=(3.6 xx 10^8 N C^(-1) (2.0 xx 10^(-8) C)) +7.2N`
towards the line charge.
Similarly, the field at the positive charge, i.e.,
at `r= 0.022 m` is
`E_2=3.3 xx 10^8 N C^(-1)`.
The force on the positive charge is
`F_2=(3.3 xx 10^8 N C^(-1) xx (2.0 xx 10^(-8) C))`
`=6.6N away from the line charge.
Hence, the net force on the dipole=(7.2-6.6)N`
`=0.6N` toward the line charge.