Calculating the Force and Torque on a current loop

[Physicslearner500039]

Homework Statement

A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50-T magnetic field, as shown in Fig.
(a) Calculate the net force and torque that the magnetic field exerts on the coil.
(b) The coil is rotated through a 30 Deg angle about the axis shown, with the left side coming out of the plane of the figure and the right side going into the plane. Calculate the net force and torque that the magnetic field now exerts on the coil.

Relevant Equations

F = IlBsin(Θ); Toque = Magnetic moment * Magnetic Field

$\vec \tau = \vec \mu \times \vec B -eq1$
$F = I \vec l \times \vec B -eq2$

The forces i have indicated

The magnetic moment is coming out of the page.
I am only attempting only the part (a) as of now
a. The force calculations are
F1 = 1.4*0.22*1.5 = 0.462 +X direction
F2 = 1.4*0.22*1.5 = -0.462 -X direction
F3 = 1.4*.35*1.5 = 0.735 +Y direction
F4 = 1.4*.35*1.5 = -0.735 -Y direction
The net force is 0.
b. The Torque as per eq1 cross product of magnetic moment and the magnetic field. Since they are 180 Deg apart, the Torque is 0. Since they are 180 Deg apart the system is unstable and the coil starts moving. Am I correct? Please advise.

 

[haruspex]

Since they are 180 Deg apart the system is unstable

Does that suffice to show instability? What if the forces were directed outwards from the loop?

 

[Physicslearner500039]

Does that suffice to show instability? What if the forces were directed outwards from the loop?

There was only a one line in the textbook that if angle between the Magnetic moment and Magnetic field is 180, it is in an unstable equilibrium. I don't know much apart from that.

Regarding the Part b problem, I am finding extremely difficult to imagine and calculate the angles. Do you recommend any mathematical textbook chapter which has such kind of problems for me to solve and gain confidence.

 

[haruspex]

if angle between the Magnetic moment and Magnetic field is 180, it is in an unstable equilibrium

Ah, ok. I thought you meant that the forces on opposite sides of the loop were 180 degrees out from each other, as in your diagram.

Regarding the Part b problem

See if the second part of http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html helps.