Magnetic Force, Moment, and Torque on Square Current Loop

[musiliu]

Homework Statement

[PLAIN]http://img521.imageshack.us/img521/5139/physicsproblem.jpg

Homework Equations

F_M in uniform magnetic field = I L x B

m = I A² where A is the area, direction given by Right Hand Rule (perpendicular to plane of loop)

T = m x B

The Attempt at a Solution

I need to know if my answers are correct..need fast confirmation/help.

a) using the 1st equation in the "Relevant equations"
i added all forces and it equaled to zero. but I am not sure if the unit vectors with
1/ sqrt(2) should play a role in the calculation.. I just used the i hat and k hat without the 1 / sqrt(2).. is this ok?

or...am i supposed to factor out the 1 / sqrt(2) for the magnitude of B so it's like 1/sqrt(2)B₀ ?

b) using 2nd equation in "Relevant Equations":

m = I₀ a² B₀ k hat

c) T = a² I₀ B₀ j hat

 

[anathema]

Hello! Your solutions are mostly correct, but there are a few things that need to be clarified.

a) In the first equation, the unit vectors should not be included in the calculation. They are simply used to indicate the direction of the force. So it is correct to use only i hat and k hat.

b) The second equation is not entirely correct. The correct equation for the magnetic moment (m) is m = I0 A2 n, where n is the unit vector perpendicular to the plane of the loop. In this case, n would be equal to 1/sqrt(2) i hat + 1/sqrt(2) k hat. So the correct equation would be m = I0 A2 (1/sqrt(2) i hat + 1/sqrt(2) k hat).

c) The third equation is also not entirely correct. The correct equation for torque (T) is T = m x B, where x represents the cross product. So the correct equation would be T = (I0 A2 (1/sqrt(2) i hat + 1/sqrt(2) k hat)) x B.

Hope this helps!