An electric dipole consists of two opposite charges each of magnitude `1.0xx10^(-6)C` separated by 2 cm. The dipole is placed in an external uniform field of `1xx10^(5)` N/C Find (i) the maximum torque exerted by the field on the dipole (ii) the work which an external agent will have to do in turning the dipole through `180^(@)` starting from the position, `theta=0^(@)`.

Explanation

Given, `q=1xx10^(-6)C,2a=2" cm"=0.02m`
`:." "p=qxx2a=(1xx10^(-6))xx0.02=2xx10^(-8)"C-m"`
Intensity of the external electric field, `E=1.0xx10^(5)" N/C"`
(i) `:. tau_("max")=pE=(2xx10^(-8))(1.0xx10^(5))=2xx10^(-3)" N-m"`
(ii) Net work done in turning the dipole from `0^(@)` to `180^(@)`,
i.e. `W=int_(0^(@))^(180^(@))taud theta=int_(0^(@))^(180^(@))pEsin thetad theta`
`=pE[-costheta]_(0^(@))^(180^(@))=-pE(cos180^(@)-cos0^(@))=2pE`
`=2xx(2xx10^(-8))(1xx10^(5))J=4xx10^(-3)J`