Work done by rectangular wire loop with current in magnetic field

1. Oct 25, 2011

syhpui2

1. The problem statement, all variables and given/known data

A rectangular wire loop of height h and width w, centered on the origin, carries current I in the direction shown in the figure. The angle between the positive x-axis and the plane of the loop is θ, defined as shown in the figure below. (When θ = 0 the loop lies in the x-z plane.) This entire region of space is filled with a uniform external magnetic field B pointing in the +x direction.

http://i.imgur.com/4V960.png

Part A
The magnitude of the work, |W|, involved in the rotation of the loop from θ = 0° to θ = 60° is:
(a) |W| = 9.09 × 10-5 J Correct Answer
(b) |W| = 2.37 × 10-4 J
(c) |W| = 4.25 × 10-4 J
(d) |W| = 5.87 × 10-4 J
(e) |W| = 8.13 × 10-4 J

Part B
When the loop rotates from θ = 0° to θ = 60°, the external magnetic field
(a) does no work on the loop.
(b) does positive work on the loop. Correct Answer
(c) does negative work on the loop.

2. Relevant equations

U= - dipole moment B cos(theta)

3. The attempt at a solution

For part A,
I tried

-( I * Area * B * cos(60)) - (-( I * Area * B * cos(0))) , however, it is wrong answer.

For part B,
I am confused about the work done by field (W) and the energy (U), what is difference?
How do I know a work is positive or negative in this case?

Thanks!