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 line charge of linear charge density `4.0 xx 10^(-4) C m^(-1)` as shown in figure (30-W4), Such that the negative charge is at a distance of `2.0 cm from the line charge. Find the force acting on the dipole.

Options

A. 7.2 N towards the line charge
B. 6.6 N away from the line charge
C. 0.6 N away from the line charge
D. 0.6 N towards the line charge.

Answer

D

Explanation

The electric field at a distance r from the line charge of linear density `lamda` is given by
`E=lamda/(2piepsilon_(0)r)`
Hence, the field at the negative charge, `E_(1)=((4.0xx10^(-4))(2xx9xx10^(9)))/0.02=3.6xx10^(8)NC^(-1)`
The force on the negative charge,
`F_(1)=(3.6xx10^(8))(2.0xx10^(-8))=7.2N` towards the line charge
Similarly, the field at the positive charge,
i.e., at r = 0.022 m is `E_(2)=3.3xx10^(8)NC^(-1)`.
The force on the positive charge,
`F_(2)=(3.3xx10^(8))xx(2.0xx10^(-8))=6.6N` away from the line charge.
Hence, the net force on the dipole = 7.2N - 6.6N
=0.6N towards the line charge