Acircular loop of wire having a radius of 5.58 cm carries a current of 0.230 a. a vector of unit length and parallel to the dipole moment of the loop is given by 0.60 – 0.80. if the loop is located in a uniform magnetic field given by = (0.140 t) + (0.109 t), find (a) the x-component, (b) the y-component, and (c) the z-component of the torque on the loop and (d) the magnetic potential energy of the

see explanation

Explanation:

Given quantities:

radius = r = 0.0558 [m]

current = I = 0.23 [A]

Now we solve this by obtaining the torque acting on the dipole

We obtain the magnetic moment vector M, first, |M| is defined as , where A is the cross-section area of the loop which is then

now the magnetic moment vector is equal to the magnetic dipole moment vector multiplied the magnitude we just obtained  

Now:

a )

b)

a) the determinant gives us:

b) the dot product gives =