Problem $1(20$ points$)$

An electric dipole consists of charges $+3e$ and $-3e$ separated by $5$ nm $.$ It is placed in a space right between three large flat sheets. First sheet has surface charge density $20\frac{C}{m^2}.$ Second one has surface charge density $40\frac{C}{m^2}.$ The third sheet has surface charge density $-20\frac{C}{m^2}.$

a$)(10$ points$)$ Using Gauss' law, determine, what is the direction and magnitude of the net Electric field generated by the sheets. If you remember the result without calculation and certain of it$,$ you may use the ready result this time.

b$)(10$ points$)$ What is the torque exerted on a dipole by the Electric field of the three sheets if the orientation of the dipole with respect to the positive $x$ direction $($regular right handed cartesian coordinate system$)$ is $-45$ and the distance from the midpoint of the dipole to each of the sheets is $1$ cm $?$

$($Use following constants and definitions: $e=-1\mathrm{.}6{10}^{-19}C,$ mikro