Work done by rectangular wire loop with current in magnetic field

[syhpui2]

Homework Statement

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.

Homework Equations

U= - dipole moment B cos(theta)

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!

 

[anathema]

Hello,

For part A, the correct equation to use is -(I * Area * B * cos(60)) - (-(I * Area * B * cos(0))). However, you need to make sure that the angle theta is in radians, not degrees. So the equation should be -(I * Area * B * cos(pi/3)) - (-(I * Area * B * cos(0))). This should give you the correct answer of 9.09 x 10^-5 J.

For part B, the work done by the external magnetic field is positive because it is in the same direction as the displacement of the loop. This means that the field is doing positive work on the loop, increasing its energy and causing it to rotate. The energy in this case is potential energy, or the energy stored in the loop due to its position in the magnetic field. The work done by the field is the change in potential energy, which is why it is positive in this case.

I hope this helps clarify things for you. Let me know if you have any other questions. Good luck with your research!