Potential Energy of an Electric Dipole

[yinx]

I understand that potential energy of an electric dipole is U(θ)=-pEcosθ where p is the dipole moment, E is the electric field and θ is the angle between vector p vector E.

However i have some doubts about its derivation.
in my readings, the work done is derived as such:

dw=t*d(theta) = -pEsin(theta)d(theta)

t = torque

followed by integration (i understand the integration)

it's mentioned that t = -pEsin(theta), because "the torque is in the direction of decreasing (theta) therefore there is a negative sign infront of it"

my question is what does it mean by the torque is in the direction of decreasing (theta)?
is there any other ways to explain why do we need to add a negative sign infront of pEsin(theta)?

 

[kuruman]

It is a restoring torque. If you increase $\theta$ either clockwise or counterclockwise, the torque will be in the opposite direction, either counterclockwise or clockwise. The negative sign in front has the same meaning as the negative sign in the restoring force of a spring $F=-kx$. If you stretch the spring, the force will be so as to contract it; if you compress the spring, the force will be so as to expand it.