Calculating Torque and Work of an Electric Dipole in a Uniform External Field

[ooohffff]

Homework Statement

An electric dipole consists of +/- Q = 330nC separated by a distance of 1200nm. The dipole is initially oriented in the -i direction (along the negative x axis). The dipole is in a uniform external electric field of E=2500j N/C Determine the following:

a) The magnitude of the torque on the dipole when it is at +165° to the +x axis
b) The work done by the electric field to rotate the dipole to an angle of +110° to the +x-axis from its initial position

Homework Equations

|T| = |P| |E| sin θ
W = U_f-U_i

The Attempt at a Solution

I get what to plug into solve the problems, but the only issue I have is that I'm not sure what θ should be in these equations because I can't really visualize between what two vectors the angle is supposed to be between? When it says it's initially oriented in the -i direction, does that mean it has already rotated 180°? I'm confused.

 

[drvrm]

I'm confused.

draw a diagram and then it will be/can be seen how your confusion stands..

 

[ooohffff]

So for a) would theta be 165°-90°=75°?

And for b) would final theta be 110°-90°=20° and initial theta be 180°-90°=90°

 

[drvrm]

So for a) would theta be 165°-90°=75°?

And for b) would final theta be 110°-90°=20° and initial theta be 180°-90°=90°

what is your theta angle ?
As you write the equation for Torque the angle theta seems to be angle between the dipole moment and electric field...
Initially your dipole moment is along -i direction and E is in j direction so are you turning the dipole through 75 degree...check from diagram.
post the diagram for us to see.

 

[haruspex]

are you turning the dipole through 75 degree...

No. Oriented at -i must mean at 180 degrees to the +x axis. It is then rotated to be at 110 degrees to the +x axis.
In part a) there is no actual rotation.

 

[haruspex]

So for a) would theta be 165°-90°=75°?

Yes.

 

[ooohffff]

Yes.

Okay, I did that and I got the right answer for a).

For b), plugging 20 degrees and 90 degrees didn't seem to work. Any ideas?

 

[haruspex]

For b), plugging 20 degrees and 90 degrees didn't seem to work.

What are the starting and finishing angles in b)?

 

[ooohffff]

What are the starting and finishing angles in b)?

Initial is 180, final is 110.

 

[ooohffff]

Initial is 180, final is 110.

That's not the answer though...

 

[drvrm]

Initial is 180, final is 110.

the angle is between dipole moment and E and the work done in rotating a dipole through an elementary angular displacement should be torque times the angle say differential element of theta.

 

[ooohffff]

the angle is between dipole moment and E and the work done in rotating a dipole through an elementary angular displacement should be torque times the angle say differential element of theta.

Oh wait, the final angle is actually 20° (165°-90°) and the initial is 90°(180°-90°), like I said previously. I found something else in my problem that was wrong, and I got the right number. My work is negative, which makes sense because it is rotating clockwise to align with the electric field, right?