Potential energy of a dipole in an electric field (TBR)

[Meredith92]

I'm a little bit confused about something TBR says on page 129 on the second physics book.

it says "if theta (angle between dipole axis and E field) =90 the electric dipole woudl be perpendicular to the electric field. in this case, the potential energy of the system is zero. If theta is 0, the electric dipole will be parallel to the electric field. the potential energy of this system would be at its most negative value. If theta=180, the electric dipole woudl be antiparallel to the electric field and the potential energy woudl be at its most positive value."

For some reason, what theyre saying isnt clicking with me. Why when the dipole is perpendicular is the potential energy zero? isnt there a maximum torque at this point? doesnt it want to move parallel to the field, which gives it a potential energy?

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[milski]

Potential energy is always relative, you have to set the 0 somewhere and it is an arbitrary choice. Setting the 0 to be when the dipole is perpendicular allows you to write the simplest formula for the potential energy, U=-p.E.cosθ

You are correct that the torque is the highest there but the highest torque does not [always] correspond to the highest potential energy. The PE is a sum of all the work that was done by the torque to get the dipole in its current position.

You start from the dipole being parallel to the field, with 0 torque and the lowest potential energy. As you turn the dipole, the torque starts to increase and you add a bit of work for every infinitesimal increase in the angle. At 90 degrees, the torque reaches its maximum and starts to decrease but you are still adding work to the previously done work, only smaller amounts now. Because of that the PE continues to increase and reaches its maximum at 180 degrees.

The same idea is applicable to force/work, force/PE, distance/velocity.

 

[Meredith92]

Okay it all is much clearer now. Thank you.

What do you mean by: The same idea is applicable to force/work, force/PE, distance/velocity.
Are you referring to the fact that potential energy is always relative?

 

[milski]

Right, velocity is also always relative but that's not what I had in mind.

I was talking about the fact that maximum potential energy and maximum force don't necessary happen at the same time. Same for maximum speed and maximum distance. If you accelerate and then slow down the distance you've traveled still increases but your maximum speed is at a point that you already passed.

 

[Meredith92]

Ohhh interesting. Makes so much sense w velocity and distance ... Really cool to apply that to torque and potential energy!
Thanks!