Find largest potential energy difference between 2 loop orientations

[Jaccobtw]

Homework Statement

A current loop with radius 20cm and current 2A is in a uniform magnetic field of 0.5T. Considering all possible orientations of the loop relative to the field, what is the largest potential energy difference (in Joules) you can find between two orientations.

Relevant Equations

$$U = -\mu \cdot B$$
$$ \mu = IA$$

I thought the largest PE difference would be when the loop's area vector is in the same direction as the magnetic field, hence cos(0) =1, minus when the loop's area vector in perpendicular to the field, cos(pi/2) = 0. Just plug in the variables and you get 0.126 joules. Did I make a mistake?

 

[nasu]

When the angle is zero the energy is at a minimum, not a maximum. See the minus sign in the formula.
The 90 degree is neither maximum nor minimum. The minimum is a negative value, equal in magnitude with the maximum value.

 

[kuruman]

If you write $U=-\vec {\mu} \cdot \vec B = -\mu~B~\cos\!\theta,~$you will see hat the minimum and maximum value of the potential energy $U$ is intimately related to the maximum and minimum value of the cosine of the angle between the two vectors.

 

[Jaccobtw]

When the angle is zero the energy is at a minimum, not a maximum. See the minus sign in the formula.
The 90 degree is neither maximum nor minimum. The minimum is a negative value, equal in magnitude with the maximum value.

Ah so its double the value then. Great!

 

[kuruman]

It is a common mistake to think that 0 is the smallest possible value of an energy. That is true only when negative values are not allowed. Here, they are.