Calculating Torque and Work on an Electric Dipole in a Uniform Electric Field

[tropskaerf]

An electric dipole in the x-y plane consists of two opposite charges with magnitudes of 2uC placed 10cm apart. The dipole is placed in an electric field of 10 N/C along the x-axis with a direction of p +45 degrees from the x axis.
1)Determine the magnitude and direction of torque on the dipole
2)How much work will you have to do to move the dipole from 45 degrees to 180 degrees.

So far i know that T= p X E which equals pEsin(theta) and I know that p = QL. Would the charge Q be equal to 2uC as described in the problem? I also don't understand why the dipole would rotate from 45 degrees to 180 degrees rather than down to 0 degrees when both of these directions would follow the electric field is this because of the orientation of the positive and negative charges?

I feel like simply plugging into pEsin(theta) to get QLEsin(theta) = 2uC*10cm*10N/C*sin(45) would be too simple to calculate the torque.

I know that work is the integration of torque between the two angles and that doing so would get me W= pE(cos(theta1)-cos(theta2)) i also feel like plugging in here to get W = -QLE(cos(theta2)-cos(theta1))= -2uC*10cm*10N/C*(cos(180)-cos(45)) would be too simple and not correct.

also, i know that many of these variables are vectors but i don't know how to display the arrows above them on here.

any help would be much appreciated

 

[tropskaerf]

nevermind i figured it out

 

[Weilin Meng]

Can you tell us how you figured it out?