Calculating Work Required to Rotate a Dipole in an Electric Field

[Calpalned]

Homework Statement

A dipole consists of charges +e and −e separated by 0.57 nm . It is in an electric field 2.6×104 N/C .
What is the work required to rotate the dipole from being oriented parallel to the field to being antiparallel to the field?

Homework Equations

PE = (dipole moment)(electric field) ## = 2.37 * 10^{-24}##
Work = ##W = PE(\cos{\theta_2}-\cos{\theta_1}) ## (From textbook)
Antiparallel = ##\theta_2 = 180 ##
Parallel = ##\theta_1 = 0 ##

The Attempt at a Solution

When I plugged the numbers for the equation for work I got ## = -4.7 * 10^{-24}## The correct answer is positive. I don't think I made any math mistakes but I can show my work if requested (plugging in numbers) if needed. Thank you very much.

 

[TSny]

Work = ##W = PE(\cos{\theta_2}-\cos{\theta_1}) ## (From textbook)

Is this the work done by the electric forces acting on the charges as the dipole rotates or is it the work done by an external agent that rotates the dipole at constant angular speed?

 

[Calpalned]

Is this the work done by the electric forces acting on the charges as the dipole rotates or is it the work done by an external agent that rotates the dipole at constant angular speed?

I think it's done by the electric field

 

[TSny]

From the textbook's derivation, you can see that they use the torque produced by the electric forces acting on the charges. So, the work they calculate is the work done by the electric forces. But your problem statement is apparently asking for the work required by an external agent, like yourself, to rotate the dipole. To hold the dipole at some angle, you would need to apply a torque that is equal but opposite to the torque due to the electric forces. If you rotate the dipole at a steady rate, your torque is still equal and opposite to the torque due to the electric forces.

 

[Calpalned]

From the textbook's derivation, you can see that they use the torque produced by the electric forces acting on the charges. So, the work they calculate is the work done by the electric forces. But your problem statement is apparently asking for the work required by an external agent, like yourself, to rotate the dipole. To hold the dipole at some angle, you would need to apply a torque that is equal but opposite to the torque due to the electric forces. If you rotate the dipole at a steady rate, your torque is still equal and opposite to the torque due to the electric forces.

Thank you so much. Now it makes sense!