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.
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?