Tutorial Exercise

A small, rigid object carries positive and negative $5\mathrm{.}50-nC$ charges. It is oriented so that the positive charge has coordinates $(-1\mathrm{.}20mm,1\mathrm{.}30mm)$ and the negative charge is at the point $(1\mathrm{.}80mm,-1\mathrm{.}30mm).$

$($a$)$ Find the electric dipole moment of the object. The object is placed in an electric field vec$(E)=(7\mathrm{.}80{10}^3(hat(i))-4\mathrm{.}90{10}^3(hat(j)))\frac{N}{C}.$

$($b$)$ Find the torque acting on the object.

$($c$)$ Find the potential nergy of the object$-$field system when the object is in this orientation.

$($d$)$ Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system.