Potential and torque of electric dipole in E field

[nthnschager]

Homework Statement

Q: A polar molecule has a dipole moment of magnitude 20 e*pm that makes an angle of 20 degrees with a uniform electric field of magnitude 3.0*10^3 N/C. FInd the magnitude of the torque on the dipole, and the potential energy of the system.

Homework Equations

torque = pE sin(theta)

where p is dipole moment and E is electric field mag.

The Attempt at a Solution

in the explanation in my book, (20 e*pm)(3*10^3)(sin20)
is reduced to (.02)(1.6*10^-19 C)(10^-9 m)(3*10^3 N/C)(sin20)
This might be a stupid question but why is 20 reduced to .02? I could not figure out what happened there.

Also, how do you minimize the potential energy when a dipole is is in an electric field? when U = -PEcos(theta), where U is potential energy, P is dipole moment, E is electric field, and theta is angle between direction of dipole moment and electric field. is pot. energy minimized when theta = zero or when theta = ninety?
In other words, I do not understand the concept of negetive potential energy. Would it be considered "minimized" when the potential energy is at zero or negetive?

 

[AvroArrow]

The metric system is used in physics, so 20 e*pm is 0.02 C m, that's why they reduced it to .02. The potential energy U is minimized when the angle θ between the dipole moment p and the electric field E is equal to zero, which corresponds to the dipole being aligned with the electric field. This is because the potential energy is proportional to the cosine of the angle θ between the dipole moment and the electric field, and the cosine is maximized when θ = 0°.